# Graph Theory and Combinatorics 1988

**Edited By**

Combinatorics has not been an established branch of mathematics for very long: the last quarter of a century has seen an explosive growth in the subject. This growth has been largely due to the doyen of combinatorialists, Paul Erdős, whose penetrating insight and insatiable curiosity has provided a huge stimulus for workers in the field. There is hardly any branch of combinatorics that has not been greatly enriched by his ideas.

This volume is dedicated to Paul Erdős on the occasion of his seventy-fifth birthday.

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### Book information

- Published: July 1989
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-87329-3

### Table of Contents

Preface (B. Bollobás). Paul Erdős at Seventy-Five (B. Bollobás). Packing Smaller Graphs into a Graph (J. Akiyama, F. Nakada, S. Tokunaga). The Star Arboricity of Graphs (I. Algor, N. Alon). Graphs with a Small Number of Distinct Induced Subgraphs (N. Alon, B. Bollobás). Extensions of Networks with Given Diameter (J.-C. Bermond, K. Berrada, J. Bond). Confluence of Some Presentations Associated with Graphs (N. Biggs). Long Cycles in Graphs with No Subgraphs of Minimal Degree 3 (B. Bollobás, G. Brightwell). First Cycles in Random Directed Graph Processes (B. Bollobás, S. Rasmussen). Trigraphs (J.A. Bondy). On Clustering Problems with Connected Optima in Euclidean Spaces (E. Boros, P.L. Hammer). Some Sequences of Integers (P.J. Cameron). 1-Factorizing Regular Graphs of High Degree - An Improved Bound (A.G. Chetwynd, A.J.W. Hilton). Graphs with Small Bandwidth and Cutwidth (F.R.K. Chung, P.D. Seymour). Simplicial Decompositions of Graphs: A Survey of Applications (R. Diestel). On the Number of Distinct Induced Subgraphs of a Graph (P. Erdős, A. Hajnal). On the Number of Partitions of n Without a Given Subsum (I) (P. Erdős, J.L. Nicolas, A. Sárközy). The First Cycles in an Evolving Graph (P. Flajolet, D.E. Knuth, B. Pittel). Covering the Complete Graph by Partitions (Z. Füredi). A Density Version of the Hales-Jewett Theorem for k = 3 (H. Furstenburg, Y. Katznelson). On the Path-Complete Bipartite Ramsey Number (R. Häggkvist). Towards a Solution of the Dinitz Problem? (R. Häggkvist). A Note on the Latin Squares with Restricted Support (R. Häggkvist). Pseudo-Random Hypergraphs (J. Haviland, A. Thomason). Bouquets of Geometric Lattices: Some Algebraic and Topological Aspects (M. Laurent, M. Deza). A Short Proof of a Theorem of Vámos on Matroid Representations (I. Leader). An On-Line Graph Coloring Algorithm with Sublinear Performance Ratio (L. Lovász, M. Saks, W.T. Trotter). The Partite Construction and Ramsey Set Systems (J. Nešetřil, V. Rödl). Scaffold Permutations (P. Rosenstiehl). Bounds on the Measurable Chromatic Number of R^{n} (L.A. Székely, N.C. Wormald). A Simple Linear Expected Time Algorithm for Finding a Hamilton Path (A. Thomason). Dense Expanders and Pseudo-Random Bipartite Graphs (A. Thomason). Forbidden Graphs for Degree and Neighbourhood Conditions (D.R. Woodall).