20.500.12556/ReVIS-11890 Graphs that admit a Hamilton path are cup-stackable Fay, Hurlbert and Tennant recently introduced a one-player game on a finite connected graph G, which they called cup stacking. Stacks of cups are placed at the vertices of G, and are transferred between vertices via stacking moves, subject to certain constraints, with the goal of stacking all cups at a single target vertex. If this is possible for every target vertex of G, then G is called stackable. In this paper, we prove that if G admits a Hamilton path, then G is stackable, which confirms several of the conjectures raised by Fay, Hurlbert and Tennant. Furthermore, we prove stackability for certain powers of bipartite graphs, and we construct graphs of arbitrarily large minimum degree and connectivity that do not allow stacking onto any of their vertices. Games in graphs Hamilton path Cartesian product Igre v grafih Hamiltonova pot Kartezijev produkt true true true Angleški jezik Slovenski jezik Neznano 2025-07-02 10:58:37 2025-07-02 10:58:37 2025-07-03 03:05:40 0000-00-00 00:00:00 2025 0 0 Nasl. z nasl. zaslona; Opis vira z dne 30. 6. 2025; Soavtorji: Arturo Merino, Torsten Mütze, Francesco Verciani; 114375; str. 1-12 Vol. 348 iss. 5 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-11-25 2024-12-15 2025-01-07 519.17 1872-681X 240797699 10.1016/j.disc.2024.114375 1-s2.0-S0012365X24005065-main.pdf 1-s2.0-S0012365X24005065-main.pdf 1 648D2DEB74134E1CB32B364C3E12B512 1de8446b17b170dc4fdbd9dbafd6068fcd21d6be0eecfcb5432647c27a2e10a4 2b3d5c2e-5723-11f0-8080-001a4af901a5 https://revis.openscience.si/Dokument.php?lang=slv&id=13786 Fakulteta za informacijske študije v Novem mestu 0 0 0