8 research outputs found
Structure theorem and algorithm on <mml:math altimg="si6.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-odd subgraph
No full textChordality and 2-factors in tough graphs
Get PDFA 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
