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CORR
2011
Springer

Acyclic and Star Colorings of Cographs

8 years 12 days ago
Acyclic and Star Colorings of Cographs
An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. We prove that every acyclic coloring of a cograph is also a star coloring and give a linear-time algorithm for finding an optimal acyclic and star coloring of a cograph. If the graph is given in the form of a cotree, the algorithm runs in O(n) time. We also show that the acyclic chromatic number, the star chromatic number, the treewidth plus one, and the pathwidth plus one are all equal for cographs.
Andrew Lyons
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Andrew Lyons
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