On powers of circular arc graphs and proper circular arc graphs
Let \(\mathcal K\) denote the class of circular arc graphs. The author gives a new proof that if a graph \(G\in {\mathcal K}\), then the power \(G^n\in {\mathcal K}\) for any positive integer \(n\). Moreover, he proves that if \(G^n\in {\mathcal K}\) then \(G^{n+2}\in {\mathcal K}\) and if \(\text{diam}(G^n)\geq 4\) then \(G^n\in {\mathcal K}\) implies \(G^{n+1}\in {\mathcal K}\). For digraphs the author gives an exact terminology and several interesting results. E.g. he proves that if a directed graph \(G^n\) belongs to the class of in-, out- or local tournaments, then \(G^{n+1}\) belongs to the same class. Moreover, the author gives an interesting discussion about possible applications, but no concrete application is given.
scientific article; zbMATH DE number 933096
scientific article