Paper Info
Title
On Clique-Transversals and Clique-Independent Sets
Abstract
A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A clique-independent set is a subset of pairwise disjoint cliques of G. Denote by tC(G) and aC(G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when tC(H)=aC(H), for every induced subgraph H of G. In this paper, we prove that every graph not containing a 4-wheel nor a 3-fan as induced subgraphs and such that every odd cycle of length greater than 3 has a short chord is clique-perfect. The proof leads to polynomial time algorithms for finding the parameters tC(G) and aC(G), for graphs belonging to this class. In addition, we prove that to decide whether or not a given subset of vertices of a graph is a clique-transversal is Co-NP-Complete. The complexity of this problem has been mentioned as unknown in the literature. Finally, we describe a family of highly clique-imperfect graphs, that is, a family of graphs G whose difference tC(G)-aC(G) is arbitrarily large.
Year
DOI
Venue
2002
10.1023/A:1021363810398
Annals OR
Keywords
DocType
Volume
clique-independent sets,clique-perfect graphs,clique-transversals,highly clique-imperfect graphs,integer linear programming,linear programming
Journal
116
Issue
ISSN
Citations 
1-4
1572-9338
22
PageRank 
References 
Authors
0.88
9
3
Name
Order
Citations
PageRank
Guillermo Durán129629.28
Min Chih Lin225921.22
Jayme Luiz Szwarcfiter361895.79