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MEDIANS OF GRAPHS AND KINGS OF TOURNAMENTS

Hai-Yen Lee, 李海晏, Gerard J. Chang and 張鎭華
Taiwanese Journal of Mathematics
Vol. 1, No. 1 (March 1997), pp. 103-110
Stable URL: http://www.jstor.org/stable/43834464
Page Count: 8
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MEDIANS OF GRAPHS AND KINGS OF TOURNAMENTS
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Abstract

We first prove that for any graph G with a positive vertex weight function w, there exists a graph H with a positive weight function wʹ such that w(v)=wʹ(v) for all vertices v in G and whose wʹ-median is G. This is a generalization of a previous result for the case in which all weights are 1. The second result is that for any n-tournament T without transmitters, there exists an integer m ≤ 2n—1 and an m-tournament Tʹ whose kings are exactly the vertices of T. This improves upon a previous result for m ≤ 2n.

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