Detecting a Theta or a Prism

A theta in a graph is an induced subgraph consisting of two nonadjacent vertices joined by three disjoint paths. A prism in a graph is an induced subgraph consisting of two disjoint triangles joined by three disjoint paths. This paper gives a polynomial-time algorithm to test whether a graph has an induced subgraph that is either a prism or a theta.

[1]  Paul D. Seymour,et al.  Recognizing Berge Graphs , 2005, Comb..

[2]  Paul D. Seymour,et al.  The three-in-a-tree problem , 2010, Comb..

[3]  Michele Conforti,et al.  Testing balancedness and perfection of linear matrices , 1993, Math. Program..

[4]  Nicolas Trotignon,et al.  Algorithms for Perfectly Contractile Graphs , 2005, SIAM J. Discret. Math..