Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable
Discrete Mathematics
2013-01-31 v1 Combinatorics
Abstract
For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. This is the problem of coloring the vertices while ensuring that two vertices that are adjacent or have a common neighbor receive different colors. It is already known that planar graphs of girth at least 6 and of maximum degree D are list 2-distance (D+2)-colorable when D>=24 (Borodin and Ivanova (2009)) and 2-distance (D+2)-colorable when D>=18 (Borodin and Ivanova (2009)). We prove here that D>=17 suffices in both cases. More generally, we show that graphs with maximum average degree less than 3 and D>=17 are list 2-distance (D+2)-colorable. The proof can be transposed to list injective (D+1)-coloring.
Cite
@article{arxiv.1301.7090,
title = {Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable},
author = {Marthe Bonamy and Benjamin Lévêque and Alexandre Pinlou},
journal= {arXiv preprint arXiv:1301.7090},
year = {2013}
}
Comments
22 pages, 5 figures, submitted