On a conjecture concerning 4-coloring of graphs with one crossing
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909578061414400 |
|---|---|
| author | Dvořák, Zdeněk Lidický, Bernard Mohar, Bojan |
| author_facet | Dvořák, Zdeněk Lidický, Bernard Mohar, Bojan |
| contents | We conjecture that every graph of minimum degree five with no separating triangles and drawn in the plane with one crossing is 4-colorable. In this paper, we use computer enumeration to show that this conjecture holds for all graphs with at most 28 vertices, explore the consequences of this conjecture and provide some insights on how it could be proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a conjecture concerning 4-coloring of graphs with one crossing Dvořák, Zdeněk Lidický, Bernard Mohar, Bojan Combinatorics 05C15 We conjecture that every graph of minimum degree five with no separating triangles and drawn in the plane with one crossing is 4-colorable. In this paper, we use computer enumeration to show that this conjecture holds for all graphs with at most 28 vertices, explore the consequences of this conjecture and provide some insights on how it could be proved. |
| title | On a conjecture concerning 4-coloring of graphs with one crossing |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2504.08327 |