A note on cycle lengths in graphs of chromatic number five and six

Abstract

In this note, we prove that every non-complete $(k+1)$-critical graph contains cycles of all lengths modulo $k$, where $k=4,5$.

arXiv admin note: text overlap with arXiv:2012.10624

References in corpus (2)

• Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs
• A strengthening on odd cycles in graphs of given chromatic number