Abstract
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)).
Original language | English |
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Pages (from-to) | 103-108 |
Number of pages | 6 |
Journal | Electronic Notes in Discrete Mathematics |
Volume | 50 |
DOIs | |
Publication status | Published - 1 Dec 2015 |
Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics