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Local medians in chordal graphs

✍ Scribed by Heiko Wittenberg


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
535 KB
Volume
28
Category
Article
ISSN
0166-218X

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## Abstract Suppose __G = (V, E)__ is a graph in which every vertex __x__ has a non‐negative real number __w(x)__ as its weight. The __w__‐distance sum of a vertex __y__ is __D~G, w~(y)__ = Οƒ~xβ‰…v~ __d(y, x)w(x).__ The __w__‐median of __G__ is the set of all vertices __y__ with minimum __w__‐distanc

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The main result of this paper is the NP-completeness of the HAMILTONIAN CIRCUIT problem for chordal bipartite graphs. This is proved by a sophisticated reduction from SATISFIABILITY. As a corollary, HAMILTONIAN CIRCUIT is NP-complete for strongly chordal split graphs. On both classes the complexity