Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04044 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- A total coloring of a graph $G$ is a coloring of the vertices and edges such that two adjacent or incident elements receive different colors. The minimum number of colors required for a total coloring of a graph $G$ is called the total chromatic number, denoted by $χ''(G)$. Let $G$ be a planar graph of maximum degree eight. It is known that $9\leq χ''(G) \leq 10$. We here prove that $χ''(G)=9$ when the graph does not contain any subgraph isomorphic to a $4$-fan.