Cycles of even lengths modulo k

Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree 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 2k - 1, which improves the previously known bound of 3k - 2. We also show that Thomassen's conjecture is true for m = 2.

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Ajit A. Diwan
• Keywords: JGT 2010, Length Congruent, Minimum Degree, Natural Numbers