Abstract
A set A of vertices of a graph G = (V, E) is an asteroidal set if for each vertex a ɛ A, the set A {a} is contained in one connected component of G−N[a]. The maximum cardinality of an asteroidal set of the graph G is said to be the asteroidal number of G. We show that there are efficient algorithms to compute the asteroidal number for claw-free graphs, HHD-free graphs, circular-arc graphs and circular permutation graphs, while the corresponding decision problem for graphs in general is NP-complete.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kloks, T., Kratsch, D., Müller, H. (1997). Asteroidal sets in graphs. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024501
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DOI: https://doi.org/10.1007/BFb0024501
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