Chordality and 2-factors in tough graphs
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 Chvtal show that for all ?>0 there exists a -tough chordal graph with no 2 -factor. Furthermore, examples due to Bauer and Schmeichel show that the result is false for 6 -chordal graphs.
68r10 05c38