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| Preface to the first edition | |
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| Preface to the second edition | |
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| Graphs | |
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| Terminology of graphs and digraphs | |
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| Eulerian circuits | |
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| Hamiltonian circuits | |
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| Trees | |
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| Cayley's theorem | |
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| Spanning trees and the greedy algorithm | |
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| Search trees | |
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| Strong connectivity | |
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| Colorings of graphs and Ramsey's theorem | |
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| Brooks' theorem | |
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| Ramsey's theorem and Ramsey numbers | |
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| The Lovasz sieve | |
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| The Erdos-Szekeres theorem | |
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| Turan's theorem and extremal graphs | |
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| Turan's theorem and extremal graph theory | |
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| Systems of distinct representatives | |
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| Bipartite graphs | |
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| P. Hall's condition | |
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| SDRs | |
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| Konig's theorem | |
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| Birkhoff's theorem | |
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| Dilworth's theorem and extremal set theory | |
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| Partially ordered sets | |
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| Dilworth's theorem | |
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| Sperner's theorem | |
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| Symmetric chains | |
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| The Erdos-Ko-Rado theorem | |
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| Flows in networks | |
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| The Ford-Fulkerson theorem | |
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| The integrality theorem | |
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| A generalization of Birkhoff's theorem | |
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| Circulations | |
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| De Bruijn sequences | |
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| The number of De Bruijn sequences | |
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| Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme | |
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| Quadratic forms | |
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| Winkler's theorem | |
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| Associative block designs | |
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| The principle of inclusion and exclusion; inversion formulae | |
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| Inclusion-exclusion | |
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| Derangements | |
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| Euler indicator | |
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| Mobius function | |
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| Mobius inversion | |
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| Burnside's lemma | |
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| Probleme des menages | |
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| Permanents | |
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| Bounds on permanents | |
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| Schrijver's proof of the Minc conjecture | |
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| Fekete's lemma | |
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| Permanents of doubly stochastic matrices | |
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| The Van der Waerden conjecture | |
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| The early results of Marcus and Newman | |
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| London's theorem | |
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| Egoritsjev's proof | |
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| Elementary counting; Stirling numbers | |
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| Stirling numbers of the first and second kind | |
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| Bell numbers | |
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| Generating functions | |
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| Recursions and generating functions | |
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| Elementary recurrences | |
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| Catalan numbers | |
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| Counting of trees | |
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| Joyal theory | |
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| Lagrange inversion | |
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| Partitions | |
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| The function P[subscript k] (n) | |
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| The partition function | |
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| Ferrers diagrams | |
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| Euler's identity | |
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| Asymptotics | |
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| The Jacobi triple product identity | |
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| Young tableaux and the hook formula | |
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| (0, 1)-Matrices | |
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| Matrices with given line sums | |
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| Counting (0, 1)-matrices | |
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| Latin squares | |
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| Orthogonal arrays | |
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| Conjugates and isomorphism | |
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| Partial and incomplete Latin squares | |
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| Counting Latin squares | |
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| The Evans conjecture | |
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| The Dinitz conjecture | |
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| Hadamard matrices, Reed--Muller codes | |
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| Hadamard matrices and conference matrices | |
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| Recursive constructions | |
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| Paley matrices | |
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| Williamson's method | |
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| Excess of a Hadamard matrix | |
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| First order Reed-Muller codes | |
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| Designs | |
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| The Erdos-De Bruijn theorem | |
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| Steiner systems | |
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| Balanced incomplete block designs | |
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| Hadamard designs | |
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| Counting | |
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| (higher) incidence matrices | |
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| The Wilson--Petrenjuk theorem | |
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| Symmetric designs | |
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| Projective planes | |
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| Derived and residual designs | |
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| The Bruck--Ryser--Chowla theorem | |
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| Constructions of Steiner triple systems | |
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| Write-once memories | |
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| Codes and designs | |
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| Terminology of coding theory | |
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| The Hamming bound | |
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| The Singleton bound | |
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| Weight enumerators and MacWilliams' theorem | |
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| The Assmus--Mattson theorem | |
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| Symmetry codes | |
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| The Golay codes | |
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| Codes from projective planes | |
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| Strongly regular graphs and partial geometries | |
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| The Bose--Mesner algebra | |
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| Eigenvalues | |
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| The integrality condition | |
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| Quasisymmetric designs | |
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| The Krein condition | |
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| The absolute bound | |
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| Uniqueness theorems | |
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| Partial geometries | |
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| Examples | |
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| Directed strongly regular graphs | |
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| Neighborhood regular graphs | |
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| Orthogonal Latin squares | |
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| Pairwise orthogonal Latin squares and nets | |
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| Euler's conjecture | |
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| The Bose--Parker--Shrikhande theorem | |
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| Asymptotic existence | |
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| Orthogonal arrays and transversal designs | |
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| Difference methods | |
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| Orthogonal subsquares | |
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| Projective and combinatorial geometries | |
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| Projective and affine geometries | |
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| Duality | |
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| Pasch's axiom | |
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| Desargues' theorem | |
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| Combinatorial geometries | |
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| Geometric lattices | |
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| Greene's theorem | |
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| Gaussian numbers and q-analogues | |
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| Chains in the lattice of subspaces | |
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| q-analogue of Sperner's theorem | |
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| Interpretation of the coefficients of the Gaussian polynomials | |
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| Spreads | |
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| Lattices and Mobius inversion | |
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| The incidence algebra of a poset | |
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| The Mobius function | |
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| Chromatic polynomial of a graph | |
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| Weisner's theorem | |
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| Complementing permutations of geometric lattices | |
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| Connected labeled graphs | |
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| MDS codes | |
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| Combinatorial designs and projective geometries | |
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| Arcs and subplanes in projective planes | |
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| Blocking sets | |
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| Quadratic and Hermitian forms | |
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| Unitals | |
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| Generalized quadrangles | |
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| Mobius planes | |
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| Difference sets and automorphisms | |
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| Block's lemma | |
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| Automorphisms of symmetric designs | |
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| Paley--Todd and Stanton--Sprott difference sets | |
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| Singer's theorem | |
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| Difference sets and the group ring | |
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| The Multiplier Theorem and extensions | |
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| Homomorphisms and further necessary conditions | |
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| Codes and symmetric designs | |
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| The sequence of codes of a symmetric design | |
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| Wilbrink's theorem | |
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| Association schemes | |
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| Examples | |
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| The eigenmatrices and orthogonality relations | |
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| Formal duality | |
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| The distribution vector of a subset | |
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| Delsarte's inequalities | |
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| Polynomial schemes | |
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| Perfect codes and tight designs | |
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| (More) algebraic techniques in graph theory | |
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| Tournaments and the Graham--Pollak theorem | |
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| The spectrum of a graph | |
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| Hoffman's theorem | |
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| Shannon capacity | |
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| Applications of interlacing and Perron--Frobenius | |
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| Graph connectivity | |
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| Vertex connectivity | |
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| Menger's theorem | |
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| Tutte connectivity | |
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| Planarity and coloring | |
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| The chromatic polynomial | |
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| Kuratowski's theorem | |
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| Euler's formula | |
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| The Five Color Theorem | |
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| List-colorings | |
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| Whitney Duality | |
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| Whitney duality | |
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| Circuits and cutsets | |
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| MacLane's theorem | |
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| Embeddings of graphs on surfaces | |
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| Embeddings on arbitrary surfaces | |
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| The Ringel--Youngs theorem | |
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| The Heawood conjecture | |
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| The Edmonds embedding technique | |
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| Electrical networks and squared squares | |
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| The matrix-tree theorem | |
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| De Bruijn sequences | |
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| The network of a squared rectangle | |
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| Kirchhoff's theorem | |
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| Polya theory of counting | |
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| The cycle index of a permutation group | |
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| Counting orbits | |
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| Weights | |
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| Necklaces | |
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| The symmetric group | |
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| Stirling numbers | |
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| Baranyai's theorem | |
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| One-factorizations of complete graphs and complete designs | |
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| Hints and comments on problems | |
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| Hints | |
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| Suggestions | |
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| Comments on the problems in each chapter | |
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| Formal power series | |
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| Formal power series ring | |
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| Formal derivatives | |
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| Inverse functions | |
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| Residues | |
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| The Lagrange--Burmann formula | |
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| Name Index | |
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| Subject Index | |