## Taiwanese Journal of Mathematics

### MEDIANS OF GRAPHS AND KINGS OF TOURNAMENTS*

#### 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 $w'$ such that $w(v)=w'(v)$ for all vertices $v$ in $G$ and whose $w'$-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 $m\leq 2n-1$ and an $m$-tournament $T'$ whose kings are exactly the vertices of $T$. This improves upon a previous result for $m\leq 2n$.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 1 (1997), 103-110.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500404928

Digital Object Identifier
doi:10.11650/twjm/1500404928

Mathematical Reviews number (MathSciNet)
MR1435500

Zentralblatt MATH identifier
0878.05029

#### Citation

Lee, Hai-Yen; Chang, Gerard J. MEDIANS OF GRAPHS AND KINGS OF TOURNAMENTS*. Taiwanese J. Math. 1 (1997), no. 1, 103--110. doi:10.11650/twjm/1500404928. https://projecteuclid.org/euclid.twjm/1500404928