Distance-two coloring of sparse graphs
✍ Scribed by Dvořák, Zdeněk; Esperet, Louis
- Book ID
- 122608932
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 387 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0195-6698
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## Abstract A proper coloring of the vertices of a graph is called a __star coloring__ if the union of every two color classes induces a star forest. The star chromatic number χ~__s__~(__G__) is the smallest number of colors required to obtain a star coloring of __G__. In this paper, we study the r
It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d 2 Âf is at most O(dÂlog f ). This is tight (up to a constant factor) for all admissible values of d and f.