Chordal co-gem-free and (P5, gem)-free graphs have bounded clique-width
نویسندگان
چکیده
منابع مشابه
Bounding the Clique-Width of H-free Chordal Graphs
A graph is H-free if it has no induced subgraph isomorphic to H . Brandstädt, Engelfriet, Le and Lozin proved that the class of chordal graphs with independence number at most 3 has unbounded clique-width. Brandstädt, Le and Mosca erroneously claimed that the gem and the co-gem are the only two 1-vertex P4-extensions H for which the class of H-free chordal graphs has bounded clique-width. In fa...
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We give a complete structure description of (P 5 ,gem)-free graphs. By the results of a related paper, this implies bounded clique width for this graph class.
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A graph is (P5,gem)-free, when it does not contain P5 (an induced path with five vertices) or a gem (a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path P4) as an induced subgraph. We present O(n2) time recognition algorithms for chordal gem-free and for (P5,gem)free graphs. Using a characterization of (P5,gem)-free graphs by their prime graphs...
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A vertex set D in a finite undirected graph G is an efficient dominating set (e.d.s. for short) of G if every vertex of G is dominated by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d.s. in G, is known to be NP-complete even for very restricted graph classes such as for 2P3-free chordal graphs while it is solvable in polynomial time for P...
متن کاملGem- And Co-Gem-Free Graphs Have Bounded Clique-Width
The P4 is the induced path of four vertices. The gem consists of a P4 with an additional universal vertex being completely adjacent to the P4, and the co-gem is its complement graph. Gemand co-gem-free graphs generalize the popular class of cographs (i. e. P4-free graphs). The tree structure and algebraic generation of cographs has been crucial for several concepts of graph decomposition such a...
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 145 شماره
صفحات -
تاریخ انتشار 2005