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- Paul Erdös, Richard Rado
- 2004

A version of Dirichlet's box argument asserts that given a positive integer a and any a2 +1 objects x0 , x1 , . . ., xa 2, there are always a+1 distinct indices v (0 < v < a 2) such that the… (More)

- Paul Erdös
- 1961

Define f (k, l) as the least integer so that every graph having f(k, 1) vertices contains either a complete graph of order k or a set of l independent vertices (a complete graph of order k is a graph… (More)

- Paul Erdös
- 1964

An r-graph is a graph whose basic elements are its vertices and r-tuples . It is proved that to every 1 and r there is an e(l, r) so that for n > no every r-graph of n vertices and n'-E(i, r)… (More)

- G. DIRAC, Paul Erdös
- 2004

In a recent paper [l] K . CORRÁDI 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, A H Stone
- 1963

Denote by G(n; m) a graph of n vertices and m edges. We prove that every G(n; [n2/4] -t I) contains a circuit of 2 edges for every 3 5 I < czn, also that every G(n; [ns/4] + 1) contams a k&, u.) with… (More)

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

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) configurations of a… (More)

- Vasek Chvátal, Paul Erdös
- Discrete Mathematics
- 1972

Proof. Let G satisfy the hypothesis of Theorem 1. Clearly, G contains a circuit ; let C be the longest one . If G has no Hamiltonian circuit, there is a vertex x with x ~ C . Since G is s-connected,… (More)

- Paul Erdös, Peter Frankl, Vojtech Rödl
- Graphs and Combinatorics
- 1986

Let H be a fixed graph of chromatic number r. It is shown that the number of graphs on n vertices and not containing H as a subgraph is 2 ( z)( '-•'i * O( ')). Let h,(n) denote the maximum number of… (More)

To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question… (More)

- Paul Erdös, JOSEPH LEHNER
- 1941

It is easily seen that the number of partitions of n having k or less summands is equal to the number of partitions of n in which no summand exceeds k . Thus the preceding results can be applied to… (More)