Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

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Graph Coloring Problems

ONAG, as the book is commonly known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.

On numbers and games, by J. H. Conway. Pp ix, 238. £6·50. 1976. SBN 0 12 186350 6 (Academic Press)

We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.

Small Ramsey Numbers

A survey of Nordhaus-Gaddum type relations

We study the complexity of finding long paths in directed or undirected graphs, Given a graph G =(V, E) and a number k our algorithm decides within time O(K! · |V| · |E|) for all u,v ɛ V Whether there exists some path of length k firm u to v. The complexity of this algorithm has to be compared with 0(|V| k−1 · |E|) Which is the worst case behaviour of the algorithms described up to now in the literature, We get similar results for the problems of finding a longest path, a cycle of length k or a longest cycle, respectively. Our approach is based on the idea of representing certain families of sets by subfamilies of small cardiality. We also discuss the border lines of this idea.

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How to Find Long Paths Efficiently

On presente un algorithme polynomial permettant de determiner un sous-graphe biparti d'un graphe G sans triangle ni boucle de degre maximum 3, contenant au moins 4/5 des aretes de G. On caracterise le dodecaedre et le graphe de Petersen comme les seuls graphes connexes 3-reguliers sans triangle ni boucle pour lesquels il n'existe pas de sous graphe biparti ayant un nombre d'aretes superieur a cette proportion

Largest bipartite subgraphs in triangle-free graphs with maximum degree three

The subchromatic number of a graph

A lower bound is established on the number of edges in a maximum k-colorable subgraph of a loopless graph G. For the special case of 3-regular graphs, lower bounds are also determined on the maximum number of edges in a bipartite subgraph whose color classes are of equal size.

Stephen C. Locke

Papers

Largest bipartite subgraphs in triangle-free graphs with maximum degree three

The subchromatic number of a graph

Maximum k-colorable subgraphs

Cycles and paths through specified vertices in k -connected graphs

The Hamilton spaces of Cayley graphs on abelian groups