6-Star-Coloring of Subcubic Graphs
✍ Scribed by Min Chen; André Raspaud; Weifan Wang
- Book ID
- 112121106
- Publisher
- John Wiley and Sons
- Year
- 2012
- Tongue
- English
- Weight
- 664 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
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## Abstract A __star coloring__ of an undirected graph __G__ is a proper vertex coloring of __G__ (i.e., no two neighbors are assigned the same color) such that any path of length 3 in __G__ is not bicolored. The __star chromatic number__ of an undirected graph __G__, denoted by χ~s~(__G__), is the
## Abstract The __square__ __G__^2^ of a graph __G__ is the graph with the same vertex set __G__ and with two vertices adjacent if their distance in __G__ is at most 2. Thomassen showed that every planar graph __G__ with maximum degree Δ(__G__) = 3 satisfies χ(__G__^2^) ≤ 7. Kostochka and Woodall c
## 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