Hierarchical complexity of 2-clique-colouring weakly chordal graphs and perfect graphs having cliques of size at least 3

Hierarchical Complexity of 2-Clique-Colouring Weakly Chordal Graphs and Perfect Graphs Having Cliques of Size at Least 3

LATIN 2014: Theoretical Informatics - Lecture Notes in Computer Science ◽

10.1007/978-3-642-54423-1_2 ◽

2014 ◽

pp. 13-23

Author(s):

Helio B. Macêdo Filho ◽

Raphael C. S. Machado ◽

Celina M. H. Figueiredo

Keyword(s):

Chordal Graphs ◽

Perfect Graphs ◽

Hierarchical Complexity

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Characterization of Super Strongly Perfect Graphs in Chordal and Strongly Chordal Graphs

Mapana Journal of Sciences ◽

10.12723/mjs.23.10 ◽

2012 ◽

Vol 11 (4) ◽

pp. 121-131 ◽

Cited By ~ 1

Author(s):

R Mary Jeya Jothi ◽

A Amutha

Keyword(s):

Dominating Set ◽

Chordal Graphs ◽

Perfect Graphs ◽

Perfect Graph ◽

Strongly Chordal Graphs ◽

Minimal Dominating Set ◽

The Relationship ◽

Odd Cycles ◽

Domination Numbers

A Graph G is Super Strongly Perfect Graph if every induced sub graph H of G possesses a minimal dominating set that meets all the maximal complete sub graphs of H. In this paper, we have investigated the characterization of Super Strongly Perfect graphs using odd cycles. We have given the characterization of Super Strongly Perfect graphs in chordal and strongly chordal graphs. We have presented the results of Chordal graphs in terms of domination and co - domination numbers γ and . We have given the relationship between diameter, domination and co - domination numbers of chordal graphs. Also we have analysed the structure of Super Strongly Perfect Graph in Chordal graphs and Strongly Chordal graphs.

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Algorithmic Aspects of Some Variations of Clique Transversal and Clique Independent Sets on Graphs

Algorithms ◽

10.3390/a14010022 ◽

2021 ◽

Vol 14 (1) ◽

pp. 22

Author(s):

Chuan-Min Lee

Keyword(s):

Planar Graphs ◽

Maximum Clique ◽

Chordal Graphs ◽

Perfect Graphs ◽

Line Graphs ◽

Np Completeness ◽

Split Graphs ◽

Transversal Numbers ◽

The Relationship ◽

Independence Numbers

This paper studies the maximum-clique independence problem and some variations of the clique transversal problem such as the {k}-clique, maximum-clique, minus clique, signed clique, and k-fold clique transversal problems from algorithmic aspects for k-trees, suns, planar graphs, doubly chordal graphs, clique perfect graphs, total graphs, split graphs, line graphs, and dually chordal graphs. We give equations to compute the {k}-clique, minus clique, signed clique, and k-fold clique transversal numbers for suns, and show that the {k}-clique transversal problem is polynomial-time solvable for graphs whose clique transversal numbers equal their clique independence numbers. We also show the relationship between the signed and generalization clique problems and present NP-completeness results for the considered problems on k-trees with unbounded k, planar graphs, doubly chordal graphs, total graphs, split graphs, line graphs, and dually chordal graphs.

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