Score sequences of bitournaments

TL;DR

This paper characterizes the score sequences of bitournaments, a special class of oriented complete bipartite graphs, by introducing the concept of sequence trimming and providing a new characterization method.

Contribution

It introduces the concept of trimming sequences and offers a novel characterization of score sequences of bitournaments.

Findings

Characterization of score sequences using trimming sequences

Extension of Moon's previous results

New criteria for score sequence validity

Abstract

The score of a vertex $x$ in an oriented graph is defined to be its outdegree, \emph{i.e.}, the number of arcs with initial vertex $x$. The score sequence of an oriented graph is the sequence of all scores arranged in nondecreasing order. An oriented complete bipartite graph is called a bitournament. The score sequence of a bitournament consists of two nondecreasing sequences of nonnegative integers, one for each of the two partite sets. Moon has characterized the score sequences of bitournaments. This paper introduces the concept of trimming a sequence and gives a characterization of score sequences of bitournaments utilizing this concept.