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, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Taiwan;No Affiliations,;Department of Computer Science and Information Engineering, National Dong Hwa University, Shoufeng, Hualien, Taiwan 97401
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

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Abstract

The $\mathcal{G}$-width of a class of graphs $\mathcal{G}$ is defined as follows. A graph G has $\mathcal{G}$-width k if there are k independent sets $\mathbb{N}_1,\dots,\mathbb{N}_{\rm \tt k}$ in G such that G can be embedded into a graph ${\rm H \in \mathcal{G}}$ such that for every edge e in H which is not an edge in G , there exists an i such that both endpoints of e are in ***i . For the class $\mathfrak{B}$ of block graphs we show that $\mathfrak{B}$-width is NP-complete and we present fixed-parameter algorithms.