Report
Improved upper bound on the Frank number of $3$-edge-connected graphs
| العنوان: | Improved upper bound on the Frank number of $3$-edge-connected graphs |
|---|---|
| المؤلفون: | Barát, János, Blázsik, Zoltán L. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | In an orientation $O$ of the graph $G$, an arc $e$ is deletable if and only if $O-e$ is strongly connected. For a $3$-edge-connected graph $G$, the Frank number is the minimum $k$ for which $G$ admits $k$ strongly connected orientations such that for every edge $e$ of $G$ the corresponding arc is deletable in at least one of the $k$ orientations. H\"orsch and Szigeti conjectured the Frank number is at most $3$ for every $3$-edge-connected graph $G$. We prove an upper bound of $5$, which improves the previous bound of $7$. Comment: 7 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.19050 |
| رقم الانضمام: | edsarx.2305.19050 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |