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Independence Number And Disjoint Theta Graphs, Shinya Fujita, Colton Magnant

Department of Mathematical Sciences Faculty Publications

The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a θ-graph to be a pair of vertices u,v with three internally disjoint paths joining u to v. Given an independence number α and a fixed integer k, the results contained in this paper provide sharp bounds on the order f(k,α) of a graph with independence number α(G)≤α which contains no k disjoint θ-graphs. Since every θ-graph contains an even cycle, these results provide k disjoint even cycles in graphs of order at least f(k,α)+1. We also discuss the relationship between this …