Abstract In this paper we consider the general Ramsey number problem for paths when the complete graph is colored with k colors. Specifically, given paths P i 1 , P i 2 ,…, P i k with i 1 , i 2 ,…, i… Expand

We characterize those pairs of forbidden subgraphs sufficient to imply various hamiltonian type properties in graphs and present a result concerning the pairs for such graphs.Expand

Let denote the class of all graphsG which satisfyG→(G1,G2). As a way of measuring minimality for members of, we define thesize Ramsey number ř(G1,G2) by.We then investigate various questions… Expand

Given a class ℒ of (so called “forbidden”) graphs, ex (n, ™) denotes the maximum number of edges a graphGn of ordern can have without containing subgraphs from ™, and the above problem is calleddegenerate extremal.Expand

In the past, Ramsey numbers were known for pairs of cycles of lengths r and s when one of the following occurred: (1) r is small, one of r or s is small relative to the other, or r is odd and r = s.Expand

We show that every graph G with n vertices and in edges contains a bipartite subgraph H such that iE(H)l>IE(G)1/2, i.e.,when F= K 3, we will prove the following.Expand

Given a family of (hyper)graphs $\mathcal{F}$ a (hyper)graph $G$ is said to be $\mathcal{F}$-saturated if $G$ is $F$-free for any $F \in\mathcal{F}$ but for any edge e in the complement of $G$ the… Expand

A new upper bound is given for the cycle-complete graph Ramsey number r(C,,,, K), the smallest order for a graph which forces it to contain either a cycle of order m or a set of ri independent vertices.Expand

Abstract For a fixed pair of integers r, s ≥ 2, all positive integers m and n are determined which have the property that if the edges of Km,n (a complete bipartite graph with parts n and m) are… Expand