Convexity and HHD-Free Graphs
نویسندگان
چکیده
It is well known that chordal graphs can be characterized via m-convexity. In this paper we introduce the notion of m-convexity (a relaxation of m-convexity) which is closely related to semisimplicial orderings of graphs. We present new characterizations of HHD-free graphs via m -convexity and obtain some results known from [B. Jamison and S. Olariu, Adv. Appl. Math., 9 (1988), pp. 364–376] as corollaries. Moreover, we characterize weak bipolarizable graphs as the graphs for which the family of all m-convex sets is a convex geometry. As an application of our results we present a simple efficient criterion for deciding whether a HHD-free graph contains a r-dominating clique with respect to a given vertex radius function r.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 12 شماره
صفحات -
تاریخ انتشار 1999