A characterization of chain probe graphs
Résumé
A chain probe graph is a graph that admits an independent set $S$ of vertices and a set $F$ of pairs of elements of $S$ such that $G+F$ is a chain graph (i.e., a $2K_2$-free bipartite graph). We show that chain probe graphs are exactly the bipartite graphs that do not contain as an induced subgraph a member of a family of six forbidden subgraphs, and deduce an $O(n^2)$ recognition algorithm.