Clique graphs of Helly circular arc graphs
@article{Durn2001CliqueGO, title={Clique graphs of Helly circular arc graphs}, author={Guillermo Dur{\'a}n and Min Chih Lin}, journal={Ars Comb.}, year={2001}, volume={60} }
Abstract: Clique graphs of several classes of graphs have been already characterized. Trees, interval graphs, chordal graphs, block graphs, clique-Helly graphs are some of them. However, no characterization of clique graphs of circular-arc graphs and some of their subclasses is known. In this paper, we present a characterization theorem of clique graphs of Helly circular-arc graphs and prove that this subclass of circular-arc graphs is contained in the intersection between proper circular-arc…
15 Citations
Algorithms for clique-independent sets on subclasses of circular-arc graphs
- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2006
NP-completeness results for edge modification problems
- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2006
A Survey on Clique Graphs
- Mathematics
- 2003
Intersection graphs, in general, have been receiving attention in graph theory, for some time. For example, there are specific papers on this subject, dated some sixty years ago. On the other hand,…
Modification Problems toward Proper (Helly) Circular-arc Graphs
- MathematicsArXiv
- 2022
We present a 9 ·nO(1)-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van ’t Hof and Villanger [Algorithmica 2013] and Crespelle et al.…
Computational aspects of the Helly property: a survey
- Mathematics, Computer ScienceJournal of the Brazilian Computer Society
- 2010
This work describes algorithms for solving different problems arising from the basic Helly property, and discusses the complexity of these problems, some of them leading to NP-hardness results.
References
SHOWING 1-10 OF 21 REFERENCES
Clique Graphs of Chordal and Path Graphs
- MathematicsSIAM J. Discret. Math.
- 1994
A special class of graphs named expanded trees is discussed, which consists of a subclass of disk-Helly graphs and it is shown that the clique graph of every chordal (hence path) graph is an expanded tree.
Algorithms on circular-arc graphs
- Mathematics, Computer ScienceNetworks
- 1974
A characterization of the circular-arc graph is given and efficient algorithms for recognizing two subclasses are described and for finding a maximum independent set, a minimum covering by cliques and a maximum clique of a circular-Arc graph are described.
A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs
- MathematicsJ. Graph Theory
- 1982
It is proved that all the classes of graphs mentioned in the title are F- graphs or F*-graphs for subsets F of a set of three digraphs.
Lexicographic orientation and representation algorithms for comparability graphs, proper circular arc graphs, and proper interval graphs
- MathematicsJ. Graph Theory
- 1995
A simple new technique is introduced which allows us to solve several problems that can be formulated as seeking a suitable orientation of a given undirected graph, and to recognize and represent proper interval graphs.
Matrix characterizations of circular-arc graphs
- Mathematics
- 1971
Abstract : A graph G is a circular-arc graph if there is a 1-1 correspondence between the vertices of G and a family of arcs on a circle such that two distinct vertices are adjacent when the…
O(M*N) Algorithms for the Recognition and Isomorphism Problems on Circular-Arc Graphs
- Mathematics, Computer ScienceSIAM J. Comput.
- 1995
The approach is to reduce the recognition problem of circular-arc graphs to that of circle graphs, which has the following advantages: it is conceptually simpler than Tucker's $O(n^3)$ recognition algorithm; it exploits the similarity between circle graphs and circular-Arc graphs in a natural fashion; it yields an isomorphism algorithm.