| Preface |
| Graphs / 1.： |
| Terminology of graphs and digraphs |
| Eulerian circuits |
| Hamiltonian circuits |
| Trees / 2.： |
| Cayley's theorem |
| Spanning trees and the greedy algorithm |
| Colorings of graphs and Ramsey's theorem / 3.： |
| Brooks' theorem |
| Ramsey's theorem and Ramsey numbers |
| The Erdos-Szekeres theorem |
| Turan's theorem and extremal graphs / 4.： |
| Turan's theorem and extremal graph theory |
| Systems of distinct representatives / 5.： |
| Bipartite graphs |
| P. Hall's condition |
| SDRs |
| Konig's theorem |
| Birkhoff's theorem |
| Dilworth's theorem and extremal set theory / 6.： |
| Partially ordered sets |
| Dilworth's theorem |
| Sperner's theorem |
| Symmetric chains |
| The Erdos-Ko-Rado theorem |
| Flows in networks / 7.： |
| The Ford-Fulkerson theorem |
| The integrality theorem |
| Ageneralization of Birkhoff's theorem |
| De Bruijn sequences / 8.： |
| The number of De Bruijn sequences |
| The addressing problem for graphs / 9.： |
| Quadratic forms |
| Winkler's theorem |
| The principle of inclusion and exclusion; inversion formulae / 10.： |
| Inclusion-exclusion |
| Derangements |
| Euler indicator |
| Mobius function |
| Mobius inversion |
| Burnside's lemma |
| Probleme des menages |
| Permanents / 11.： |
| Bounds on permanents |
| Schrijver's proof of the Minc conjecture |
| Fekete's lemma |
| Permanents of doubly stochastic matrices |
| The Van der Waerden conjecture / 12.： |
| The early results of Marcus and Newman |
| London's theorem |
| Egoritsjev's proof |
| Elementary counting; Stirling numbers / 13.： |
| Stirling numbers of the first and second kind |
| Bell numbers |
| Generating functions |
| Recursions and generating functions / 14.： |
| Elementary recurrences |
| Catalan numbers |
| Counting of trees |
| Joyal theory |
| Lagrange inversion |
| Partitions / 15.： |
| The function Pk(n) |
| The partition function |
| Ferrers diagrams |
| Euler's identity |
| Asymptotics |
| The Jacobi triple product identity |
| Young tableaux and the hook formula |
| (0,1)-Matrices / 16.： |
| Matrices with given line sums |
| Counting (0,1)-matrices |
| Latin squares / 17.： |
| Orthogonal arrays |
| Conjugates and isomorphism |
| Partial and incomplete latin squares |
| Counting Latin squares |
| The Evans conjecture |
| Hadamard matrices, Reed-Muller codes / 18.： |
| Hadamard matrices and conference matrices |
| Recursive constructions |
| Paley matrices |
| Williamson's method |
| Excess of a Hadamard matrix |
| First order Reed-Muller codes |
| Designs / 19.： |
| The Erdos-De Bruijn theorem |
| Steiner systems |
| Balanced incomplete block designs |
| Hadamard designs |
| Counting, (higher) incidence matrices |
| The Wilson-Petrenjuk theorem |
| Symmetric designs |
| Projective planes |
| Derived and residual designs |
| The Bruck-Ryser-Chowla theorem |
| Constructions of Steiner triple systems |
| Write-once memories |
| Codes and designs / 20.： |
| Terminology of coding theory |
| The Hamming bound |
| The Singleton bound |
| Weight enumerators and MacWilliams' theorem |
| The Assmus-Mattson theorem |
| Symmetry codes |
| The Golay codes |
| Codes from projective planes |
| Strongly regular graphs and partial geometries / 21.： |
| The Bose-Mesner algebra |
| Eigenvalues |
| The integrality condition |
| Quasisymmetric designs |
| The Krein condition |
| The absolute bound |
| Uniqueness theorems |
| Partial geometries |
| Examples |
| Orthogonal Latin squares / 22.： |
| Pairwise orthogonal Latin squares and nets |
| Euler's conjecture |
| The Bose-Parker-Shrikhande theorem |
| Asymptotic existence |
| Orthogonal arrays and transversal designs |
| Dlifference methods, orthogonal subsquares |
| Projective and combinatorial geometries / 23.： |
| Projective and affine geometries |
| Quality |
| Pasch's axiom |
| Desargues' theorem |
| Combinatorial geometries |
| Geometric lattices |
| Greene's theorem |
| Gaussian numbers and q-analogues / 24.： |
| Chains in the lattice of subspaces, q-analogue of Sperner's theorem |
| Interpretation of the coefficients of the Gaussian polynomials |
| Spreads |
| Lattices and Mobius inversion / 25.： |
| The incidence algebra of a poset |
| The Mobius function, chromatic polynomial of a graph |
| Weisner's theorem |
| Complementing permutations of geometric lattices |
| Connected labeled graphs |
| Combinatorial designs and projective geometries / 26.： |
| Arcs and subplanes in projective planes |
| Blocking sets |
| Quadratic and Hermitian forms |
| Unitals |
| Generalized quadrangles |
| Mobius planes |
| Difference sets and automorphisms / 27.： |
| Automorphisms of symmetric designs |
| Paley-Todd and Stanton-Sprott difference sets |
| Singer's theorem |
| Difference sets and the group ring / 28.： |
| The Multiplier Theorem and extensions |
| Homomorphisms and further necessary conditions |
| Codes and symmetric designs / 29.： |
| The sequence of codes of a symmetric design |
| Wilbrink's theorem |
| Association schemes / 30.： |
| Examples, the eigenmatrices and orthogonality relations |
| Formal duality, the distribution vector of a subset |
| Delsarte's inequalities |
| Polynomial schemes |
| Perfect codes and tight designs |
| Algebraic graph theory: eigenvalue techniques / 31.： |
| Tournaments and the Graham-Pollak theorem |
| The spectrum of a graph |
| Hoffman's theorem |
| Shannon capacity |
| Applications of interlacing and Perron-Frobenius |
| Graphs: planarity and duality / 32.： |
| Deletion and contraction |
| The chromatic polynomial, Euler's formula |
| Whitney duality, matroids |
| Graphs: colorings and embeddings / 33.： |
| The Five Color Theorem, embeddings and colorings on arbitrary surfaces |
| The Heawood conjecture |
| The Edmonds embedding technique |
| Electrical networks and squared squares / 34.： |
| The matrix-tree theorem |
| The network of a squared rectangle |
| Kirchhoff's theorem |
| Polya theory of counting / 35.： |
| The cycle index of a permutation group |
| Counting orbits |
| Weights, necklaces, the symmetric group |
| Stirling numbers |
| Baranyai's theorem / 36.： |
| One-factorizations of complete graphs and complete designs |
| Hints and comments on problems / Appendix 1.： |
| Hints |
| Suggestions |
| Comments on the problems in each chapter |
| Formal power series / Appendix 2.： |
| Formal power series ring, formal derivatives |
| Inverse functions |
| Residues |
| The Lagrange-Burmann formula |
| Name Index |
| Subject Index |
| Preface to the first edition |
| Preface to the second edition |
| Search trees |
| Strong connectivity |
| The Lovasz sieve |
| A generalization of Birkhoff's theorem |
| Circulations |
| Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme |
| Associative block designs |
| The function P[subscript k] (n) |
| (0, 1)-Matrices |
| Counting (0, 1)-matrices |
| Partial and incomplete Latin squares |
| The Dinitz conjecture |
| Hadamard matrices, Reed--Muller codes |
| Counting |
| (higher) incidence matrices |
| The Wilson--Petrenjuk theorem |
| The Bruck--Ryser--Chowla theorem |
| The Assmus--Mattson theorem |
| The Bose--Mesner algebra |
| Directed strongly regular graphs |
| Neighborhood regular graphs |
| The Bose--Parker--Shrikhande theorem |
| Difference methods |
| Orthogonal subsquares |
| Duality |
| Chains in the lattice of subspaces |
| q-analogue of Sperner's theorem |
| The Mobius function |
| Chromatic polynomial of a graph |
| MDS codes |
| Block's lemma |
| Paley--Todd and Stanton--Sprott difference sets |
| The eigenmatrices and orthogonality relations |
| Formal duality |
| The distribution vector of a subset |
| (More) algebraic techniques in graph theory |
| Tournaments and the Graham--Pollak theorem |
| Applications of interlacing and Perron--Frobenius |
| Graph connectivity |
| Vertex connectivity |
| Menger's theorem |
| Tutte connectivity |
| Planarity and coloring |
| The chromatic polynomial |
| Kuratowski's theorem |
| Euler's formula |
| The Five Color Theorem |
| List-colorings |
| Whitney Duality |
| Whitney duality |
| Circuits and cutsets |
| MacLane's theorem |
| Embeddings of graphs on surfaces |
| Embeddings on arbitrary surfaces |
| The Ringel--Youngs theorem |
| Weights / 37.： |
| Necklaces |
| The symmetric group |
| Formal power series ring / 38.： |
| Formal derivatives |
| The Lagrange--Burmann formula |
| Preface |
| Graphs / 1.： |
| Terminology of graphs and digraphs |
図書
