Chordality and 2-factors in tough graphs


Bauer, D. and Katona, G.Y. and Kratsch, D. and Veldman, H.J. (2000) Chordality and 2-factors in tough graphs. Discrete Mathematics, 99 (1-3). pp. 323-329. ISSN 0012-365X

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Abstract:A graph G is chordal if it contains no chordless cycle of length at least four and is k-chordal if a longest chordless cycle in G has length at most k. In this note it is proved that all ..-tough 5-chordal graphs have a 2-factor. This result is best possible in two ways. Examples due to Chvátal show that for all ε>0 there exists a (..-ε)-tough chordal graph with no 2-factor. Furthermore, examples due to Bauer and Schmeichel show that the result is false for 6-chordal graphs.
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Copyright:© 2000 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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