Cycles of even lengths modulo k |
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| Authors: | Ajit A. Diwan |
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| Affiliation: | Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India |
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| Abstract: | 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 |
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| Keywords: | cycle lengths minimum degree |
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