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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
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Characterizing forbidden pairs for hamiltonian properties
TLDR
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
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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
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On a class of degenerate extremal graph problems
TLDR
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
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All Ramsey numbers for cycles in graphs
TLDR
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
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How to make a graph bipartite
TLDR
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
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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
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On cycle - Complete graph ramsey numbers
TLDR
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
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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
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Path-cycle Ramsey numbers
TLDR
In this paper, the Ramsey numbers are obtained for all path-cycle pairs. Expand
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