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**public sources and our publisher partners.**2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set… Expand

The present note consists of some remarks on graphs. A graph G is a set of points some of which are connected by edges. We assume here that no two points are connected by more than one edge. The… Expand

A well-known theorem of Ramsay (8; 9) states that to every n there exists a smallest integer g(n) so that every graph of g(n) vertices contains either a set of n independent points or a complete… Expand

AbstractAnr-graph is a graph whose basic elements are its vertices and r-tuples. It is proved that to everyl andr there is anε(l, r) so that forn>n0 everyr-graph ofn vertices andnr−ε(l, r) r-tuples… Expand

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,… Expand

In this paper G(n ; I) will denote a graph of n vertices and l edges, K„ will denote the complete graph of p vertices G (p ; (PA and K,(p i , . . ., p,) will denote the rchromatic graph with p i… Expand

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)… Expand