WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Recognition of probe distance-hereditary graphs
Discrete Applied Mathematics
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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 驴1,...,驴 k in G such that G can be embedded into a graph $H \in \mathcal{G}$ with the property 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 驴 i . For the class $\mathfrak{T}\mspace{-1.5mu}\mathfrak{P}$ of trivially-perfect graphs we show that $\mathfrak{T}\mspace{-1.5mu}\mathfrak{P}$-width is NP-complete and we present fixed-parameter algorithms.