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In a recent paper [l] K . CORRADI and A. HAJNAL proved that if a finite graph without multiple edges contains at least 3k vertices and the valency of every vertex is at least 2k, where k is a… (More)

- Paul Erdös, András Hajnal
- Discrete Applied Mathematics
- 1989

Abstract In this paper we will consider Ramsey-type problems for finite graphs, r -partitions and hypergraphs. All these problems ask for the existence of large homogeneous (monochromatic)… (More)

A gruph consists of a finite set of vertices some pairs of which are adjacent, i.e., joined by an edge. No edge joins a vertex to itself and at most one edge joins any two vertices. The degree of a… (More)

1. INTRODUCTION In this paper our main object is the study of relations between cardinal numbers which are written in the form a-(b o , b,,. . .) r or a-(b)C ~° or (b) (b o b,) Such relations were… (More)

- András Hajnal, Wolfgang Maass, Pavel Pudlák, Mario Szegedy, György Turán
- 28th Annual Symposium on Foundations of Computer…
- 1987

We examine a powerful model of parallel computation: polynomial size threshold circuits of bounded depth (the gates compute threshold functions with polynomial weights). Lower bounds are given to… (More)

(1) n → (k1, . . . , k`)` means that if we split the r-tuples of a set, S, |S| = n into ` classes, than for some i, 1 ≤ i ≤ ` there is a subset Si ⊆ S, |Si| ≥ ki all of whose r-tuples are in the i-th… (More)

Fundamentals about Partition Relations. Trees and Positive Ordinary Partition Relations. Negative Ordinary Partition Relations and the Discussion of the Finite Case. The Canonization Lemmas. Large… (More)

- Paul Erdös, Zoltán Füredi, András Hajnal, Péter Komjáth, Vojtech Rödl, Ákos Seress
- Discrete Mathematics
- 1986

Abstract Let G be a graph, m > r ⩾1 integers. Suppose that it has a good coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r… (More)

- Paul Erdös, András Hajnal, Vera T. Sós, Endre Szemerédi
- Combinatorica
- 1983

The paper deals with common generalizations of classical results of Ramsey and Turán. The following is one of the main results. Assumek≧2, ε>0,Gn is a sequence of graphs ofn-vertices and at least… (More)

- András Hajnal
- 1965