A Note on Edge-Group Choosability of Planar Graphs without 5-Cycles

Abstract

This paper is devoted to a study of the concept of edge-group choosability of graphs. We say that $G$ is edge- $k$ -group choosable if its line graph is $k$ -group choosable. In this paper, we study an edge-group choosability version of Vizing conjecture for planar graphs without 5-cycles and for planar graphs without noninduced 5-cycles (2010 Mathematics Subject Classification: 05C15, 05C20).