تقرير
Maximum spread of $K_{2,t}$-minor-free graphs
| العنوان: | Maximum spread of $K_{2,t}$-minor-free graphs |
|---|---|
| المؤلفون: | Linz, William, Lu, Linyuan, Wang, Zhiyu |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | The spread of a graph $G$ is the difference between the largest and smallest eigenvalues of the adjacency matrix of $G$. In this paper, we consider the family of graphs which contain no $K_{2,t}$-minor. We show that for any $t\geq 2$, there is an integer $\xi_t$ such that the maximum spread of an $n$-vertex $K_{2,t}$-minor-free graph is achieved by the graph obtained by joining a vertex to the disjoint union of $\lfloor \frac{2n+\xi_t}{3t}\rfloor$ copies of $K_t$ and $n-1 - t\lfloor \frac{2n+\xi_t}{3t}\rfloor$ isolated vertices. The extremal graph is unique, except when $t\equiv 4 \mod 12$ and $\frac{2n+ \xi_t} {3t}$ is an integer, in which case the other extremal graph is the graph obtained by joining a vertex to the disjoint union of $\lfloor \frac{2n+\xi_t}{3t}\rfloor-1$ copies of $K_t$ and $n-1-t(\lfloor \frac{2n+\xi_t}{3t}\rfloor-1)$ isolated vertices. Furthermore, we give an explicit formula for $\xi_t$. Comment: Minor revisions. arXiv admin note: text overlap with arXiv:2209.13776 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2212.05540 |
| رقم الأكسشن: | edsarx.2212.05540 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |