Another proof of Moon's theorem on generalised tournament score sequences

Abstract

Landau \cite{Landau1953} showed that a sequence $(d_i{)}_{i=1}^n$ of integers is the score sequence of some tournament if and only if ${\sum }_{i\in J}{d}_i\ge \left(\genfrac{}{}{0ex}{}{|J|}{2}\right)$ for all $J\subseteq \{1,2,\dots ,n\}$, with equality if $|J|=n$. Moon \cite{Moon63} extended this result to generalised tournaments. We show how Moon's result can be derived from Landau's result.

6 pages

References in corpus (1)

• Eplett's theorem for self-converse generalised tournaments

Cited by in corpus (1)

• Eplett's theorem for self-converse generalised tournaments