A clock is a cycle with a vertex that has exactly two neighbors on the cycle. We show that (triangle, cube, clock)-free graphs of girth at least 9 always contain a vertex of degree 2, partially answering to a conjecture of Trotignon. As a second result, we show that the class of clock-free graphs is χ-bounded by max(4, ω(G)).
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics