## A Tribute to Paul ErdosThis volume is dedicated to Paul Erdos, who profoundly influenced mathematics in the twentieth century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks was the host of stimulating problems and conjectures, to many of which he attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'! Eminent mathematicians from around the world have contributed articles to this volume that reflect the diversity of Erdos' interests, and it will be a fund of insight for number theorists, combinatorialists, set theorists and analysts. |

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### Contents

1 | |

Sumfree subsets | 13 |

Is there a different proof of the ErdosRado theorem? | 27 |

Almost collinear triples among N points on the plane | 39 |

Hamilton cycles in random graphs of minimal degree at least k | 59 |

The circumference of a graph with a given minimal degree | 97 |

On arithmetic progressions in sums of sets of integers | 105 |

On graphs not containing prescribed induced subgraphs | 111 |

On scentered posets | 307 |

A GalvinHajnal conjecture on uncountably chromatic graphs | 313 |

Necessary conditions for mean convergence of HermiteFejér interpolation | 317 |

On the ErdosFuchs theorems | 331 |

A tournament which is not finitely representable | 339 |

On the volume of the spheres covered by a random walk | 341 |

Special Lucas sequences including the Fibonacci sequence modulo a prime | 349 |

A remark on heights of subspaces | 359 |

Partitions sans petits sommants | 121 |

A compact sequential space | 153 |

The critical parameter for connectedness of some random graphs | 161 |

III The large moduli | 177 |

Locally finite groups of permutations of N acting on l8 | 195 |

Hypergraph games and the chromatic number | 201 |

On arithmetic graphs associated with integral domains | 207 |

On the number of certain subgraphs of graphs without large cliques and independent subsets ... | 223 |

Sets of multiples of Behrend sequences | 249 |

A functional equation arising from mortality tables | 259 |

The differences between consecutive primes IV | 277 |

On the cofinality of countable products of cardinal numbers | 289 |

Incompactness for chromatic numbers of graphs | 361 |

Graphs with no unfriendly partitions | 373 |

On the greatest prime factor of an arithmetical progression | 385 |

Sperner Turan and Bregman revisited | 391 |

On the mean convergence of derivatives of Lagrange interpolation | 397 |

Sur une question dErdos et Schinzel | 405 |

Large apreserving sets in infinite aconnected graphs | 445 |

Some recent results on interpolation | 451 |

Partitioning the quadruples of topological spaces | 459 |

Some of my favourite unsolved problems | 467 |

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### Common terms and phrases

Abelian group assume choose chromatic number cofinal complete graph completes the proof con condition conjecture connected constant construction contains contradiction convergence Corollary countable d'aprčs deduce define Démonstration denote disjoint edges elements entiers equation ER-function Erdos exists finite fixed follows function f graph G Hajnal Hamilton cycles Hence holds hypergraph implies induced subgraphs induction inequality infinite integers interpolation isomorphic Lemma lemme Let G limit ordinal logn Math MG(X minimal degree multiplicative nombre non-trivial non-zero notation number theory obtain ordinal orthogonal polynomials pairs partition Paul Erdos permutations polynomials poset premiers prime problem Proof Let proof of Lemma proof of Theorem Proposition prove random graphs regular cardinal result satisfies Section sequential space solution subgraph sum-free sum-free subset supp(da Suppose Theorem 3.1 théorčme tion ultrafilter uncountable upper bound vertex set vertices