تقرير
Group Connectivity under $3$-Edge-Connectivity
| العنوان: | Group Connectivity under $3$-Edge-Connectivity |
|---|---|
| المؤلفون: | Han, Miaomiao, Li, Jiaao, Li, Xueliang, Wang, Meiling |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C21, 05C40, 05C15 |
| الوصف: | Let $S,T$ be two distinct finite Abelian groups with $|S|=|T|$. A fundamental theorem of Tutte shows that a graph admits a nowhere-zero $S$-flow if and only if it admits a nowhere-zero $T$-flow. Jaeger, Linial, Payan and Tarsi in 1992 introduced group connectivity as an extension of flow theory, and they asked whether such a relation holds for group connectivity analogy. It was negatively answered by Hu\v{s}ek, Moheln\'{i}kov\'{a} and \v{S}\'{a}mal in 2017 for graphs with edge-connectivity 2 for the groups $S=\mathbb{Z}_4$ and $T=\mathbb{Z}_2^2$. In this paper, we extend their results to $3$-edge-connected graphs (including both cubic and general graphs), which answers open problems proposed by Hu\v{s}ek, Moheln\'{i}kov\'{a} and \v{S}\'{a}mal(2017) and Lai, Li, Shao and Zhan(2011). Combining some previous results, this characterizes all the equivalence of group connectivity under $3$-edge-connectivity, showing that every $3$-edge-connected $S$-connected graph is $T$-connected if and only if $\{S,T\}\neq \{\mathbb{Z}_4,\mathbb{Z}_2^2\}$. Comment: to appear in Journal of Graph Theory |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2009.06867 |
| رقم الأكسشن: | edsarx.2009.06867 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |