Totally odd immersions in line graphs

Andrea Jiménez; Daniel A. Quiroz; Christopher Thraves Caro

doi:10.1016/j.disc.2023.113862

Totally odd immersions in line graphs

Combinatorics 2024-02-13 v1

Authors: Andrea Jiménez , Daniel A. Quiroz , Christopher Thraves Caro

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Abstract

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

Keywords

hadwiger conjecture graph theory

Cite

@article{arxiv.2305.07752,
  title  = {Totally odd immersions in line graphs},
  author = {Andrea Jiménez and Daniel A. Quiroz and Christopher Thraves Caro},
  journal= {arXiv preprint arXiv:2305.07752},
  year   = {2024}
}

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4 pages

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