Extending total colorings in planar graphs
Combinatorics
2025-09-24 v1
Abstract
We initiate the study of total-coloring extensions, and focus our attention on planar graphs, asking: ``When can a total--coloring of some subgraph of a planar graph be extended to a total--coloring of ?'' We prove that if is a matching, then any total--coloring of in extends to provided ; this number of colors is best-possible without introducing a distance condition on . We also prove that if is a set of distance-3 cliques then any total--coloring of extends to provided ; this distance condition cannot be lowered.
Cite
@article{arxiv.2509.18940,
title = {Extending total colorings in planar graphs},
author = {Owen Henderschedt and Jessica McDonald},
journal= {arXiv preprint arXiv:2509.18940},
year = {2025}
}