Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647667 | Discrete Mathematics | 2013 | 10 Pages |
Abstract
An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if a path of length two exists between them. Let Ïi(G) be the injective chromatic number of a graph G. In this paper, we investigate the injective coloring of planar graphs with girth 6. We improve some results of Borodin and Ivanova (2011) [1], Doyon et al. (2010) [4] and Li and Xu (2012) [6] by showing that if G is a planar graph with girth at least 6, then (1) Ïi(G)â¤Î+3; (2) Ïi(G)â¤Î+2 if Îâ¥9; (3) Ïi(G)â¤Î+1 if Îâ¥17.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Wei Dong, Wensong Lin,