On Directed and Undirected Diameters of Vertex-Transitive Graphs Full article
| Journal |
Combinatorica
ISSN: 0209-9683 , E-ISSN: 1439-6912 |
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| Output data | Year: 2024, Volume: 44, Pages: 1353–1366 Pages count : 14 DOI: 10.1007/s00493-024-00120-4 | ||
| Tags | 20B25, Primary 05C12, Secondary 05C20 | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
Adirected diameter of a directed graph is the maximum possible distance between a pair of vertices, where paths mustrespect edgeorientations, while undirected diameter is the diameter of the undirected graph obtained by symmetrizing the edges. In 2006 Babai proved that for a connected directed Cayley graph on n vertices the directed diameter is bounded above by a polynomial in undirected diameter and logn. Moreover, Babai conjectured that a similar bound holds for vertex-transitive graphs. We prove this conjecture of Babai, in fact, it follows from a more general bound for connected relations of homogeneous coherent configurations. The main novelty of the proof is a generalization of Ruzsa’s triangle inequality from additive combinatorics to the setting of graphs
Cite:
Skresanov S.V.
On Directed and Undirected Diameters of Vertex-Transitive Graphs
Combinatorica. 2024. V.44. P.1353–1366. DOI: 10.1007/s00493-024-00120-4 WOS Scopus РИНЦ OpenAlex
On Directed and Undirected Diameters of Vertex-Transitive Graphs
Combinatorica. 2024. V.44. P.1353–1366. DOI: 10.1007/s00493-024-00120-4 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jan 23, 2024 |
| Accepted: | Jun 27, 2024 |
| Published online: | Jul 9, 2024 |
| Published print: | Nov 20, 2024 |
Identifiers:
| Web of science: | WOS:001268956800001 |
| Scopus: | 2-s2.0-85197801234 |
| Elibrary: | 68767018 |
| OpenAlex: | W4400465025 |