Abstract
This paper describes a decomposition scheme for coloring perfect graphs. Based on this scheme, one need only concentrate on coloring highly connected (at least 3-connected) perfect graphs. This idea is illustrated on planar perfect graphs, which yields a straightforward coloring algorithm. We suspect that, under appropriate definition, highly connected perfect graphs might possess certain regular properties that are amenable to coloring algorithms.
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This research has been supported in part by National Science Foundation under grant ECS—8105989 to Northwestern University.
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Hsu, W.L. Coloring planar perfect graphs by decomposition. Combinatorica 6, 381–385 (1986). https://doi.org/10.1007/BF02579263
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DOI: https://doi.org/10.1007/BF02579263