A list analog of Vizing's Theorem for simple graphs with triangles but no other odd cycles

TL;DR

This paper aimed to extend Vizing's Theorem to simple graphs containing triangles but no other odd cycles, exploring list-edge-colouring properties in such graphs.

Contribution

It proposed a list-analog of Vizing's Theorem specifically for graphs with triangles and no other odd cycles, building on prior work by Peterson and Woodall.

Findings

The paper was withdrawn by the author.

It discussed existing results on graphs without certain odd cycles.

No new results were published due to withdrawal.

Abstract

This paper has been withdrawn by the author. Peterson and Woodall previously proved that the list-edge-colouring conjecture holds for graphs without odd cycles of length 5 or longer. D. Peterson and D. R. Woodall, Edge-choosability in line-perfect multigraphs, Discrete Mathematics 202 (1999), 191-199. D. Peterson and D. R. Woodall, Erratum to "Edge-choosability in line-perfect multigraphs", Discrete Mathematics 260 (2003), 323-326.