• Publications
  • Influence
Path Ramsey numbers in multicolorings
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 ,…, iExpand
  • 92
  • 22
Characterizing forbidden pairs for hamiltonian properties
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
  • 114
  • 21
The size Ramsey number
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 questionsExpand
  • 172
  • 20
  • PDF
On a class of degenerate extremal graph problems
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
  • 75
  • 18
All Ramsey numbers for cycles in graphs
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
  • 184
  • 17
How to make a graph bipartite
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
  • 69
  • 11
  • PDF
A Survey of Minimum Saturated Graphs
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 $G$ theExpand
  • 100
  • 9
  • PDF
On cycle - Complete graph ramsey numbers
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
  • 66
  • 9
  • PDF
Path-path Ramsey-type numbers for the complete bipartite graph
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) areExpand
  • 48
  • 7
Path-cycle Ramsey numbers
In this paper, the Ramsey numbers are obtained for all path-cycle pairs. Expand
  • 49
  • 6