Cycles of even lengths modulo k

Cycles of even lengths modulo k

Thomassen [J Graph Theory 7 (1983), 261–271] conjectured that for all positive integers k and m, every graph of minimum degree at least k+1 contains a cycle of length congruent to 2m modulo k. We prove that this is true for k⩾2 if the minimum degree is at least 2k−1, which improves the previously kn...

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Veröffentlicht in:Journal of graph theory 2010-11, Vol.65 (3), p.246-252
1. Verfasser: Diwan, Ajit A.
Format: Artikel
Sprache:eng
Schlagworte:
cycle lengths
minimum degree
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Zusammenfassung:Thomassen [J Graph Theory 7 (1983), 261–271] conjectured that for all positive integers k and m, every graph of minimum degree at least k+1 contains a cycle of length congruent to 2m modulo k. We prove that this is true for k⩾2 if the minimum degree is at least 2k−1, which improves the previously known bound of 3k−2. We also show that Thomassen's conjecture is true for m = 2. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 246–252, 2010
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.20477