On an interval (1, 1)-coloring of incidentors of interval colorable graphs

Abstract

A graph is called interval colorable if there exists its proper edge coloring such that for every vertex the set of colors used for coloring the edges incident with the vertex forms an interval. A subdivision of a graph is a graph obtained by replacing each edge with a path of length 2. Petrosyan and Khachatryan posed a conjecture that the subdivision of every interval colorable graph is interval colorable. In this paper we prove this conjecture.