Block-graph width

Authors:
Maw-Shang Chang;Ling-Ju Hung;Ton Kloks;Sheng-Lung Peng
Affiliations:
Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi 62107, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi 62107, Taiwan;-;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien 97401, Taiwan
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

Let G be a class of graphs. A graph G has G-width k if there are k independent sets N"1,...,N"k in G such that G can be embedded into a graph H@?G such that for every edge e in H which is not an edge in G, there exists an i such that both endvertices of e are in N"i. For the class B of block graphs we show that graphs with B-width at most 4 are perfect. We also show that B-width is NP-complete and show that it is fixed-parameter tractable. For the class C of complete graphs, similar results are also obtained.