A Note On Acyclic Token Sliding Reconfiguration Graphs of Independent Sets
| Autor: | Avis, David, Hoang, Duc A. |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Ars Combinatoria 159:133-154, 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.61091/ars159-12 |
| Popis: | We continue the study of token sliding reconfiguration graphs of independent sets initiated by the authors in an earlier paper (arXiv:2203.16861). Two of the topics in that paper were to study which graphs $G$ are token sliding graphs and which properties of a graph are inherited by a token sliding graph. In this paper we continue this study specializing on the case of when $G$ and/or its token sliding graph $\mathsf{TS}_k(G)$ is a tree or forest, where $k$ is the size of the independent sets considered. We consider two problems. The first is to find necessary and sufficient conditions on $G$ for $\mathsf{TS}_k(G)$ to be a forest. The second is to find necessary and sufficient conditions for a tree or forest to be a token sliding graph. For the first problem we give a forbidden subgraph characterization for the cases of $k=2,3$. For the second problem we show that for every $k$-ary tree $T$ there is a graph $G$ for which $\mathsf{TS}_{k+1}(G)$ is isomorphic to $T$. A number of other results are given along with a join operation that aids in the construction of $\mathsf{TS}_k(G)$-graphs. Comment: 19 pages, 13 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|