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

Authors:
Andreas Brandstädt;Dieter Kratsch
Affiliations:
Fachbereich Informatik, Universität Rostock, A.-Einstein-Str. 21, D-18051 Rostock, Germany;Université de Metz, Laboratoire d'Informatique Théorique et Appliquée, 57045 Metz Cedex 01, France
Venue:
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Year:
2005

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Abstract

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. Hereby, as usual, the P"5 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 P"4a,b,c,d with edges ab,bc,cd plus a universal vertex e adjacent to a,b,c,d.