Combinatorics, Geometry and Probability: A Tribute to Paul Erdös

Cover......Page 1
Frontmatter......Page 2
Contents......Page 6
Preface......Page 10
Farewell to Paul Erdos......Page 12
Toast to Paul Erdos......Page 14
List of Contributors......Page 18
Paul Erdos: Some Unsolved Problems......Page 24
Menger's Theorem for a Countable Source Set......Page 34
On Extremal Set Partitions in Cartesian Product Spaces......Page 46
Matchings in Lattice Graphs and Hamming Graphs......Page 56
Reconstructing a Graph from its Neighborhood Lists......Page 74
Threshold Functions for H-factors......Page 86
A Rate for the Erdos--Turán Law......Page 94
Deterministic Graph Games and a Probabilistic Intuition......Page 104
On Oriented Embedding of the Binary Tree into the Hypercube......Page 118
Potential Theory on Distance-Regular Graphs......Page 130
On the Length of the Longest Increasing Subsequence in a Random Permutation......Page 144
On Richardson's Model on the Hypercube......Page 152
Random Permutations: Some Group-Theoretic Aspects......Page 162
Ramsey Problems with Bounded Degree Spread......Page 168
Hamilton Cycles in Random Regular Digraphs......Page 176
On Triangle Contact Graphs......Page 188
A Combinatorial Approach to Complexity Theory via Ordinal Hierarchies......Page 202
Lattice Points of Cut Cones......Page 216
The Growth of Infinite Graphs: Boundedness and Finite Spreading......Page 240
Amalgamated Factorizations of Complete Graphs......Page 246
Ramsey Size Linear Graphs......Page 264
Turán--Ramsey Theorems and Kp-Independence Numbers......Page 276
Nearly Equal Distances in the Plane......Page 306
Clique Partitions of Chordal Graphs......Page 314
On Intersecting Chains in Boolean Algebras......Page 322
On the Maximum Number of Triangles in Wheel-Free Graphs......Page 328
Blocking Sets in SQS(2v)......Page 342
(1,2)-Factorizations of General Eulerian Nearly Regular Graphs......Page 352
Oriented Hamilton Cycles in Oriented Graphs......Page 362
Minimization Problems for Infinite n-Connected Graphs......Page 378
On Universal Threshold Graphs......Page 398
Image Partition Regularity of Matrices......Page 416
Extremal Graph Problems for Graphs with a Color-Critical Vertex......Page 444
A Note on [GREEK SMALL LETTER OMEGA]1 -> [GREEK SMALL LETTER OMEGA]1 Functions......Page 458
Topological Cliques in Graphs......Page 462
Local-Global Phenomena in Graphs......Page 472
On Random Generation of the Symmetric Group......Page 486
On Vertex-Edge-Critically n-Connected Graphs......Page 494
On a Conjecture of Erdos and Cudakov......Page 510
A Random Recolouring Method for Graphs and Hypergraphs......Page 512
Obstructions for the Disk and the Cylinder Embedding Extension Problems......Page 516
A Ramsey-Type Theorem in the Plane......Page 548
The Enumeration of Self-Avoiding Walks and Domains on a Lattice......Page 558
An Extension of Foster's Network Theorem......Page 564
Randomised Approximation in the Tutte Plane......Page 572
On Crossing Numbers, and some Unsolved Problems......Page 580