| Title: | Graphs that admit a Hamilton path are cup-stackable |
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| Authors: | ID Gregor, Petr (Author)
ID Merino, Arturo (Author)
ID Mütze, Torsten (Author)
ID Verciani, Francesco (Author) |
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| Files: |  1-s2.0-S0012365X24005065-main.pdf (778,41 KB)
MD5: 648D2DEB74134E1CB32B364C3E12B512
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FIŠ - Faculty of Information Studies in Novo mesto
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| Abstract: | 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. |
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| Keywords: | Games in graphs, Hamilton path, Cartesian product |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 25.11.2024 |
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| Article acceptance date: | 15.12.2024 |
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| Publication date: | 07.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-12 |
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| Numbering: | iss. 5, Vol. 348 |
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| PID: | 20.500.12556/ReVIS-11890  |
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| COBISS.SI-ID: | 240797699 |
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| UDC: | 519.17 |
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| ISSN on article: | 1872-681X |
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| DOI: | 10.1016/j.disc.2024.114375 |
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| Note: | Nasl. z nasl. zaslona;
Opis vira z dne 30. 6. 2025;
Soavtorji: Arturo Merino, Torsten Mütze, Francesco Verciani;
114375;
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| Publication date in ReVIS: | 02.07.2025 |
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| Views: | 32 |
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| Downloads: | 0 |
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