Clique-independent sets of Helly circular-arc graphs

Durán, Guillermo; Lin, Min Chih; Mera, Sergio; Szwarcfiter, Jayme Luiz

doi:10.1016/j.endm.2004.06.016

Cited by 10 publications

(15 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Every cliqueHelly graph that contains an induced 3-sun H must contain an induced K 1,3 [24,25]. In [20] it is not only proved that K (HCA) ⊂ PCA, but also it is proved that every graph in K (HCA) is clique-Helly. Therefore, graphs in K (HCA) contain no induced 3-sun, because K 1,3 is not a PCA graph.…”

Section: Characterization Of Clique Graphs Of Hca Graphsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 94%

“…Partial results concerning these problems have been reported in [20,21], respectively. In relation to characterizing clique graphs of HCA graphs, in [20] it is proved that K (HCA) ⊂ PCA ∩ HCA thus the class is K -closed. The same paper also describes characterizations for the clique graphs of HCA graphs, but these characterizations did not lead to a polynomial time recognition algorithm, and the complexity of recognizing clique graphs of HCA graphs remained so far open.…”

Section: Introductionmentioning

confidence: 94%

“…In this sense, the characterizations are very similar to those of Hedman for K (I) and K (PI) graphs. Recall that K (HCA) ⊂ PCA [20]. For the characterizations we need to describe the PCA models of the clique graphs, both for HCA and for PHCA graphs.…”

Section: Characterization Of Clique Graphs Of Hca Graphsmentioning

confidence: 99%

See 3 more Smart Citations

The clique operator on circular-arc graphs

Lin

Soulignac

Szwarcfiter

2010

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tA circular-arc graph G is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model is called a Helly (resp. proper Helly) circular-arc graph. The clique graph K (G) of a graph G is the intersection graph of its cliques. The iterated clique graph K i (G) of G is defined by K 0 (G) = G and K i+1 (G) = K (K i (G)). In this paper, we consider two problems on clique graphs of circular-arc graphs. The first is to characterize clique graphs of Helly circular-arc graphs and proper Helly circular-arc graphs. The second is to characterize the graph to which a general circular-arc graph K -converges, if it is K -convergent. We propose complete solutions to both problems, extending the partial results known so far. The methods lead to linear time recognition algorithms, for both problems.

show abstract

Section: Characterization Of Clique Graphs Of Hca Graphsmentioning

confidence: 98%