Isoperimetry in product graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912121872187392 |
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| author | Diskin, Sahar Samotij, Wojciech |
| author_facet | Diskin, Sahar Samotij, Wojciech |
| contents | In this short note, we establish an edge-isoperimetric inequality for arbitrary product graphs. Our inequality is sharp for subsets of many different sizes in every product graph. In particular, it implies that the $2^d$-element sets with smallest edge-boundary in the hypercube are subcubes and is only marginally weaker than the Bollobás$\unicode{x2013}$Leader edge-isoperimetric inequalities for grids and tori. Additionally, it improves two edge-isoperimetric inequalities for products of regular graphs proved by Erde, Kang, Krivelevich, and the first author and answers two questions about edge-isoperimetry in powers of regular graphs raised in their work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isoperimetry in product graphs Diskin, Sahar Samotij, Wojciech Combinatorics In this short note, we establish an edge-isoperimetric inequality for arbitrary product graphs. Our inequality is sharp for subsets of many different sizes in every product graph. In particular, it implies that the $2^d$-element sets with smallest edge-boundary in the hypercube are subcubes and is only marginally weaker than the Bollobás$\unicode{x2013}$Leader edge-isoperimetric inequalities for grids and tori. Additionally, it improves two edge-isoperimetric inequalities for products of regular graphs proved by Erde, Kang, Krivelevich, and the first author and answers two questions about edge-isoperimetry in powers of regular graphs raised in their work. |
| title | Isoperimetry in product graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.02058 |