Abstract
A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. A graph G is clique-perfect if the sizes of a minimum clique-transversal and a maximum clique-independent set are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. Another open question concerning clique-perfect graphs is the complexity of the recognition problem. Recently we were able to characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs. These characterizations lead to polynomial time recognition of clique-perfect graphs in these classes of graphs. In this paper we solve the characterization problem in two new classes of graphs: diamond-free and Helly circular-arc (HCA) graphs. This last characterization leads to a polynomial time recognition algorithm for clique-perfect HCA graphs.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3485-3499 |
| Number of pages | 15 |
| Journal | Discrete Mathematics |
| Volume | 309 |
| Issue number | 11 |
| DOIs | |
| State | Published - Jun 6 2009 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
Keywords
- Clique-perfect graphs
- Diamond-free graphs
- Helly circular-arc graphs
- K-perfect graphs
- Perfect graphs