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 |