A characterization of graphs with vertex cover six

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Abstract

The complete list of forbidden minors (obstructions) for the family of graphs with vertex cover 6 have been found. This paper shows how one can limit the search space of graphs and how to simplify the process for deciding whether a graph is an obstruction for k{Vertex Cover. The upper bounds 2k + 1 (2k + 2) on the maximum number of vertices for connected (disconnected) obstructions are shown to be sharp for all k > 0.

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Dinneen, M. J., & Xiong, L. (2000). A characterization of graphs with vertex cover six. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1858, pp. 180–192). Springer Verlag. https://doi.org/10.1007/3-540-44968-x_18

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