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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228197
Cayley partial cubes
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This thesis explores partial cubes, a well-studied class of graphs that can be isometrically embedded into hypercubes, with a particular focus on those that are also Cayley graphs. A central result is a modern and mostly self-contained reconstruction of the proof that Cayley graphs of finite Coxeter groups are partial cubes, clarifying a classical but often fragmented argument. The second major contribution is the construction of non-Coxeter Cayley partial cubes, built from perfect codes in finite fields. These examples demonstrate that not all Cayley partial cubes arise from Coxeter groups, refuting a long-standing conjecture.
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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Kolja Knauer
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JAÉN GUEDES, Daniel. Cayley partial cubes. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/228197