An improved spectral lower bound of treewidth
| Autor: | Gima, Tatsuya, Hanaka, Tesshu, Noro, Kohei, Ono, Hirotaka, Otachi, Yota |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that for every $n$-vertex graph with at least one edge, its treewidth is greater than or equal to $n \lambda_{2} / (\Delta + \lambda_{2}) - 1$, where $\Delta$ and $\lambda_{2}$ are the maximum degree and the second smallest Laplacian eigenvalue of the graph, respectively. This lower bound improves the one by Chandran and Subramanian [Inf. Process. Lett., 2003] and the subsequent one by the authors of the present paper [IEICE Trans. Inf. Syst., 2024]. The new lower bound is almost tight in the sense that there is an infinite family of graphs such that the lower bound is only $1$ less than the treewidth for each graph in the family. Additionally, using similar techniques, we also present a lower bound of treewidth in terms of the largest and the second smallest Laplacian eigenvalues. Comment: 6 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
|