On Competition Polysemy and \(m\)-Competition Polysemy

Abstract

In \(2004\), Fischermann et al. \([2]\) generalized bound polysemy to competition polysemy by using digraphs instead of posets. They provided a characterization of competition polysemic pairs and a characterization of the connected graphs \(G\) for which there exists a tree \(T\) such that \((G,T)\) is competition polysemic. In this paper, we continue to study the competition polysemy and characterize the connected graphs \(G\) for which there exists a triangle-free unicyclic graph \(G’\) such that \((G,G’)\) is competition polysemic. Furthermore,we generalize competition polysemy to \(m\)-competition polysemy and
prove a characterization of \(m\)-competition polysemic pairs.