## Abstract On the model of the cycle‐plus‐triangles theorem, we consider the problem of 3‐colorability of those 4‐regular hamiltonian graphs for which the components of the edge‐complement of a given hamiltonian cycle are non‐selfcrossing cycles of constant length ≥ 4. We show that this problem is
4-Colorable 6-regular toroidal graphs
✍ Scribed by Hong-Gwa Yeh; Xuding Zhu
- Book ID
- 104113316
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 259 KB
- Volume
- 273
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
This paper proves two conjectures of Collins, Fisher and Hutchinson about the chromatic number of some circulant graphs. As a consequence, we characterize 4-colorable 6-regular toroidal graphs.
📜 SIMILAR VOLUMES
## Abstract P. Erdős conjectured in [2] that __r__‐regular 4‐critical graphs exist for every __r__ ≥ 3 and noted that no such graphs are known for __r__ ≥ 6. This article contains the first example of a 6‐regular 4‐critical graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 286–291, 2002
An L-list coloring of a graph G is a proper vertex coloring in which every vertex v gets a color from a list L(v) of allowed colors. G is called k-choosable if all lists L(v) have exactly k elements and if G is L-list colorable for all possible assignments of such lists. Verifying conjectures of Erd