The subchromatic number of a graph
Discrete Mathematics - Graph colouring and variations
The complexity of G-free colourability
Proceedings of an international symposium on Graphs and combinatorics
Graph Subcolorings: Complexity and Algorithms
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Computing
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
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A 2-subcolouring of a graph is a partition of the vertices into two subsets, each inducing a P3-free graph, i.e., a disjoint union of cliques. We give the first polynomial time algorithm to test whether a chordal graph has a 2-subcolouring. This solves (for two colours) an open problem of Broersma, Fomin, Nešetřil, and Woeginger, who gave an O(n5) time algorithm for interval graphs. Our algorithm for the larger class of chordal graphs has complexity only O(n3).