On 1-rotational decompositions of complete graphs into tripartite graphs

Abstract

Consider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let $G$ be a tripartite graph with $n$ edges, one of which is a pendent edge. This paper introduces a labeling on such a graph $G$ used to achieve 1-rotational $G$-decompositions of $K_{2nt}$ for any positive integer $t$. It is also shown that if $G$ with a pendent edge is the result of adding an edge to a path on $n$ vertices, then $G$ admits such a labeling.