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ALGORITHMICA
2006

Planar Graph Coloring Avoiding Monochromatic Subgraphs: Trees and Paths Make It Difficult

9 years 11 months ago
Planar Graph Coloring Avoiding Monochromatic Subgraphs: Trees and Paths Make It Difficult
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem. We present a complete picture for the case with a single forbidden connected (induced or noninduced) subgraph. The 2-coloring problem is NP-hard if the forbidden subgraph is a tree with at least two edges, and it is polynomially solvable in all other cases. The 3-coloring problem is NP-hard if the forbidden subgraph is a path with at least one edge, and it is polynomially solvable in all other cases. We also derive results for several forbidden sets of cycles. In particular, we prove that it is NP-complete to decide if a planar graph can be 2-colored so that no cycle of length at most 5 is monochromatic.
Hajo Broersma, Fedor V. Fomin, Jan Kratochví
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where ALGORITHMICA
Authors Hajo Broersma, Fedor V. Fomin, Jan Kratochvíl, Gerhard J. Woeginger
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