On edge-group choosability of graphs

TL;DR

This paper investigates the edge-group choosability property of graphs, exploring its relation to the line graph and proposing a version of Vizing's conjecture, with evidence from various classes of graphs.

Contribution

It introduces the concept of edge-group choosability, relates it to line graphs, and proposes an edge-group version of Vizing's conjecture supported by multiple graph classes.

Findings

Graphs with maximum degree less than 4 are edge-group choosable.

Planar graphs with maximum degree at least 11 are edge-group choosable.

Certain planar and outerplanar graphs support the conjecture.

Abstract

In this paper, we study 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. An edge-group choosability version of Vizing conjecture is given. The evidence of our claim are graphs with maximum degree less than 4, planar graphs with maximum degree at least 11, planar graphs without small cycles, outerplanar graphs and near-outerplanar graphs.