Journal of University of Science and Technology of China ›› 2021, Vol. 51 ›› Issue (5): 374-381.DOI: 10.52396/JUST-2021-0119

• Research Articles: Mathematics • Previous Articles     Next Articles

Cycle lengths in graphs of chromatic number five and six

Huo Qingyi*   

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • Received:2021-04-17 Revised:2021-05-25 Online:2021-05-31 Published:2021-12-01
  • Contact: * E-mail: qyhuo@mail.ustc.edu.cn

Abstract: A problem was proposed by Moore and West to determine whether every (k+1)-critical non-complete graph has a cycle of length 2 modulo k. We prove a stronger result that for k=4, 5, every (k+1)-critical non-complete graph contains cycles of all lengths modulo k.

Key words: cycle length, chromatic number, minimum degree, breadth-first search tree

CLC Number: