Consecutive Edge-Colorings of Generalized $θ$ -Graphs - Zhao, Yongqiang; Chang, Gerard J. (Computational Geometry, Graphs and Applications, 2011)
A proper edge-coloring of a graph G using positive integers as colors is said to be a consecutive edge-coloring if for each vertex the colors of edges incident form an interval of integers. Recently, Feng and Huang studied the consecutive edge-coloring of generalized θ-graphs. A generalized θ-graph is a graph consisting of m internal disjoint (u,v)-paths, where 2 ≤ m < ∞. This paper investigates a problem provided by Feng and Huang, and gives a positive answer to the problem, except two cases are left.