Kevin Cattell, Michael J. Dinneen. A Characterization of Graphs with Vertex Cover up to Five. In Vincent Bouchitté, Michel Morvan, editors, Orders, Algorithms, and Applications, International Workshop ORDAL 94, Lyon, France, July 4-8, 1994, Proceedings. Volume 831 of Lecture Notes in Computer Science, pages 86-99, Springer, 1994.
For the family of graphs with fixed-size vertex cover $k$, we present all of the forbidden minors (obstructions), for $k$ up to five. We derive some results, including a practical finite-state recognition algorithm, needed to compute these obstructions.