Totally odd immersions in line graphs

Andrea Jiménez; Daniel A. Quiroz; Christopher Thraves Caro

doi:10.1016/j.disc.2023.113862

paper

Totally odd immersions in line graphs

arXiv:2305.07752 · doi:10.1016/j.disc.2023.113862

Abstract

The immersion-analogue of Hadwiger's Conjecture states that every graph $G$ contains an immersion of $K_{χ (G)}$ . This conjecture has been recently strengthened in the following way: every graph $G$ contains a totally odd immersion of $K_{χ (G)}$ . We prove this stronger conjecture for line graphs of constant-multiplicity multigraphs, thus extending a result of Guyer and McDonald.

4 pages