1. Intersecting Longest Cycles in Archimedean Tilings.
- Author
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Nadeem, Muhammad Faisal, Iqbal, Hamza, Siddiqui, Hafiz Muhammad Afzal, and Azeem, Muhammad
- Subjects
- *
GRAPH connectivity , *MATERIALS science , *QUANTUM mechanics , *INTERSECTION graph theory , *PATHS & cycles in graph theory , *SUBGRAPHS , *TILING (Mathematics) - Abstract
In 1966 Gallai asked the following question: Do all longest paths (cycles) of a connected graph contain a common vertex? After a positive answer to Gallai's question, another question has been raised, Is there any family of graphs without Gallai's property? Menke found one such family, the square lattices. Embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and often used in quantum mechanics and material sciences. In this paper, we prove the existence of graphs with the empty intersection of their longest cycles as subgraphs of Archimedean lattices. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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