Cycles of even lengths modulo k
Ajit A. Diwan · Journal of Graph Theory · 2010
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