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

A graph is interval colorable if it has a proper edge coloring such that for every vertex the colors used for coloring edges adjacent to it form an interval. A subdivision of a graph is a graph obtained by substituting a path of length two for each edge. P. Petrosyan and H. Khachatrian posed a conjecture that the subdivision of each interval colorable graph is interval colorable. In this paper, we prove this conjecture. Bibliogr. 19.