{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T00:27:09Z","timestamp":1720657629837},"reference-count":0,"publisher":"Combinatorial Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>We continue the study of Token Sliding (reconfiguration) graphs of independent sets initiated by the authors in an earlier paper [Graphs Comb. 39.3, 59, 2023]. 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 in 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\\)-graphs.<\/jats:p>","DOI":"10.61091\/ars159-12","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:41Z","timestamp":1720588481000},"page":"133-154","source":"Crossref","is-referenced-by-count":0,"title":["A Note on Acyclic Token Sliding Reconfiguration Graphs of Independent Sets"],"prefix":"10.61091","volume":"159","author":[{"given":"David","family":"Avis","sequence":"first","affiliation":[]},{"name":"Graduate School of Informatics, Kyoto University, Japan","sequence":"first","affiliation":[]},{"given":"Duc A.","family":"Hoang","sequence":"additional","affiliation":[]},{"name":"VNU University of Science, Vietnam National University, Hanoi, Vietnam","sequence":"additional","affiliation":[]}],"member":"39747","published-online":{"date-parts":[[2024,6,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:53Z","timestamp":1720588493000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-159\/a-note-on-acyclic-token-sliding-reconfiguration-graphs-of-independent-sets\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,6,30]]},"published-print":{"date-parts":[[2024,6,30]]}},"URL":"https:\/\/doi.org\/10.61091\/ars159-12","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,30]]}}}