Gem- And Co-Gem-Free Graphs Have Bounded Clique-Width

Chordal co-gem-free and (P5, gem)-free graphs have bounded clique-width

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...

On the structure of (P5, gem)-free graphs

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.

On Efficient Domination for Some Classes of H-Free Chordal Graphs

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...

Algorithmic Aspects of Switch Cographs

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n) decomposition algorithm and we take advantage of the involution modular decomposition tree to state several algorithmic results. Cographs are the graphs that are totally decomposable w.r.t modular decomp...