Elsevier

Discrete Applied Mathematics

Volume 145, Issue 2, 15 January 2005, Pages 155-166
Discrete Applied Mathematics

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

https://doi.org/10.1016/j.dam.2004.01.009Get rights and content
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Abstract

We give a complete structure description of (P5,gem)-free graphs. By the results of a related paper, this implies bounded clique width for this graph class. Hereby, as usual, the P5 is the induced path with five vertices a,b,c,d,e and four edges ab,bc,cd,de, and the gem consists of a P4 a,b,c,d with edges ab,bc,cd plus a universal vertex e adjacent to a,b,c,d.

Keywords

(P5
gem)-free graphs
Modules and homogeneous sets in graphs
Prime graphs
Modular decomposition
Clique width

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Supported by LORIA Nancy, France.