تقرير
The Core Conjecture of Hilton and Zhao II: a Proof
| العنوان: | The Core Conjecture of Hilton and Zhao II: a Proof |
|---|---|
| المؤلفون: | Cao, Yan, Chen, Guantao, Jing, Guangming, Shan, Songling |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | A simple graph $G$ with maximum degree $\Delta$ is overfull if $|E(G)|>\Delta \lfloor |V(G)|/2\rfloor$. The core of $G$, denoted $G_{\Delta}$, is the subgraph of $G$ induced by its vertices of degree $\Delta$. Clearly, the chromatic index of $G$ equals $\Delta+1$ if $G$ is overfull. Conversely, Hilton and Zhao in 1996 conjectured that if $G$ is a simple connected graph with $\Delta\ge 3$ and $\Delta(G_\Delta)\le 2$, then $\chi'(G)=\Delta+1$ implies that $G$ is overfull or $G=P^*$, where $P^*$ is obtained from the Petersen graph by deleting a vertex. Cariolaro and Cariolaro settled the base case $\Delta=3$ in 2003, and Cranston and Rabern proved the next case $\Delta=4$ in 2019. In this paper, we give a proof of this conjecture for all $\Delta\ge 4$. Comment: This is the second split of arXiv:2004.00734, and is the sequel to arXiv:2108.03549. arXiv admin note: substantial text overlap with arXiv:2004.00734 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2108.04399 |
| رقم الأكسشن: | edsarx.2108.04399 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |