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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.05372 |
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| _version_ | 1866911195325267968 |
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| author | Collins, Karen L. Galvin, David Kelley, Christine A. McMillon, Emily Redlich, Amanda |
| author_facet | Collins, Karen L. Galvin, David Kelley, Christine A. McMillon, Emily Redlich, Amanda |
| contents | Graphs that are squares under the gluing algebra arise in the study of homomorphism density inequalities such as Sidorenko's conjecture. Recent work has focused on these homomorphism density applications. This paper takes a new perspective and focuses on the graph properties of arbitrary square graphs, not only those relevant to homomorphism conjectures and theorems.
We develop a set of necessary and/or sufficient conditions for a graph to be square. We apply these conditions to categorize several classical families of graphs as square or not. In addition, we create infinite families of square graphs by proving that joins and Cartesian, direct, strong, and lexicographic products of square graphs with arbitrary graphs are square. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Graphs as Algebraic Squares Collins, Karen L. Galvin, David Kelley, Christine A. McMillon, Emily Redlich, Amanda Combinatorics 05C75 (Primary), 05C76 (Secondary) Graphs that are squares under the gluing algebra arise in the study of homomorphism density inequalities such as Sidorenko's conjecture. Recent work has focused on these homomorphism density applications. This paper takes a new perspective and focuses on the graph properties of arbitrary square graphs, not only those relevant to homomorphism conjectures and theorems. We develop a set of necessary and/or sufficient conditions for a graph to be square. We apply these conditions to categorize several classical families of graphs as square or not. In addition, we create infinite families of square graphs by proving that joins and Cartesian, direct, strong, and lexicographic products of square graphs with arbitrary graphs are square. |
| title | Characterizing Graphs as Algebraic Squares |
| topic | Combinatorics 05C75 (Primary), 05C76 (Secondary) |
| url | https://arxiv.org/abs/2510.05372 |