A semi-induced subgraph characterization of upper domination perfect graphs

International audience We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs. We initiate a graph-theoretic study of subgraphs of q-proper interval graphs with maximum clique size k+1 and give an equivalent characterization of these graphs by restricted path-decomposition. By allowing the parameter q to vary from 0 to k, we obtain a nested hierarchy of graph families, from graphs of bandwidth at most k to graphs of pathwidth at most k. Allowing both parameters to vary, we have an infinite lattice of graph classes ordered by containment.

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A forbidden induced subgraph characterization of distance-hereditary 5-leaf powers

Discrete Mathematics ◽

10.1016/j.disc.2008.10.025 ◽

2009 ◽

Vol 309 (12) ◽

pp. 3843-3852 ◽

Cited By ~ 8

Author(s):

Andreas Brandstädt ◽

Van Bang Le ◽

Dieter Rautenbach

Keyword(s):

Induced Subgraph ◽

Forbidden Induced Subgraph

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A Characterization of b-Perfect Graphs

Journal of Graph Theory ◽

10.1002/jgt.20635 ◽

2011 ◽

Vol 71 (1) ◽

pp. 95-122 ◽

Cited By ~ 15

Author(s):

Chính T. Hoàng ◽

Frédéric Maffray ◽

Meriem Mechebbek

Keyword(s):

Perfect Graphs

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On the maximum q-colourable induced subgraph problem in perfect graphs

International Journal of Mathematics in Operational Research ◽

10.1504/ijmor.2010.029686 ◽

2010 ◽

Vol 2 (1) ◽

pp. 1

Author(s):

Nicola Apollonio ◽

Massimiliano Caramia

Keyword(s):

Perfect Graphs ◽

Induced Subgraph

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Structural properties of super strongly perfect graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500532 ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850053

Author(s):

T. E. Soorya ◽

Sunil Mathew

Keyword(s):

Structural Properties ◽

Dominating Set ◽

Perfect Graphs ◽

Induced Subgraph ◽

Minimal Dominating Set

A graph [Formula: see text] is super strongly perfect if every induced subgraph [Formula: see text] of [Formula: see text] possesses a minimal dominating set meeting all the maximal cliques of [Formula: see text]. Different structural properties of super strongly perfect graphs are studied in this paper. Some of the special categories of super strongly perfect graphs are identified and characterized. Certain operations of super strongly perfect graphs are also discussed towards the end.

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