Three-coloring and list three-coloring of graphs without induced paths on seven vertices
نویسندگان
چکیده
In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1, 2, 3}, and gives an explicit coloring if one exists. Moreover, we present an independent algorithm that works in the special case when triangles are forbidden in addition to induced seven-vertex paths. Its running time is significantly faster compared to the general case.
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