Browsing by Author "Hwang, SF"

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k-neighborhood-covering and -independence problems for chordal graphs
(1998-11-01)
Hwang, SF
;
Chang, GJ
;
應用數學系
;
Department of Applied Mathematics
Suppose G = (V, E) is a simple graph and k is a fixed positive integer. A vertex z k-neighborhood-covers an edge (x, y) if d(z, x) less than or equal to k and d(z, y) less than or equal to k. A k-neighborhood-covering set is a set C of vertices such that every edge in E is k-neighborhood-covered by some vertex in C. A k-neighborhood-independent set is a set of edges in which no two distinct edges can be k-neighborhood-covered by the same vertex in V. In this paper we first prove that the neighborhood-covering and the k-neighborhood-independence problems are NP-complete for chordal graphs. We then present a linear-time algorithm for finding a minimum k-neighborhood-covering set and a maximum k-neighborhood-independent set for a strongly chordal graph provided that a strong elimination ordering is given in advance.