A Characterization of Graphs with Vertex Cover Six

Michael J. Dinneen, Liu Xiong. A Characterization of Graphs with Vertex Cover Six. In Ding-Zhu Du, Peter Eades, Vladimir Estivill-Castro, Xuemin Lin, Arun Sharma, editors, Computing and Combinatorics, 6th Annual International Conference, COCOON 2000, Sydney, Australia, July 26-28, 2000, Proceedings. Volume 1858 of Lecture Notes in Computer Science, pages 180-192, Springer, 2000. [doi]


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 \VC{k}. The upper bounds $2k+1$ ($2k+2$) on the maximum number of vertices for connected (disconnected) obstructions are shown to be sharp for all $k > 0$.