Independence Number and Disjoint Theta Graphs

Authors

• Shinya Fujita, Maebashi Institute of TechnologyFollow
• Colton Magnant, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2011

Publication Title

The Electronic Journal of Combinatorics

ISSN

1077-8926

Abstract

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 problem and a generalized ramsey problem involving sets of graphs.

Comments

Copyright of the article remains with the author. Article obtained from the Electronic Journal of Combinatorics.

Recommended Citation

Fujita, Shinya, Colton Magnant. 2011. "Independence Number and Disjoint Theta Graphs." The Electronic Journal of Combinatorics, 18 (1): 1-27. source: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p150
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/117

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