ON INTERVAL EDGE-COLORINGS OF COMPLETE MULTIPARTITE GRAPHS

A graph $G$ is called a complete $r$-partite $(r\geq 2)$ graph, if its vertices can be divided into $r$ non-empty independent sets $V_1,\ldots,V_r$ in way that each vertex $V_i$ adjacent to all the other $V_j$ for $1\leq i<j\leq r$. Let $K_{n_{1},n_{2},\ldots,n_{r}}$ denote with $V_1,V_2,\ldots,V_r$ of sizes $n_{1},n_{2},\ldots,n_{r}$. An edge-coloring colors $1,2,\ldots,t$ an \emph{interval $t$-coloring}, are used and edges incident distinct form interval integers. In this paper we have obtained some results on existence construction edge-colorings graphs. Moreover, also derived upper bound number colorings multipartite