On two problems concerning the geodesic transversal number of graphs

We establish sharp upper and lower bounds on the geodesic transversal number of hypercubes. We also obtain a lower bound on the geodesic transversal number of Hamming graphs. As applications, we provide negative answers to two open problems concerning the geodesic transversal number.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39298
Primary Topic
Advanced Graph Theory Research
Type
preprint
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preprint

On two problems concerning the geodesic transversal number of graphs

马儇龙, Shi Chen, Tingzeng Wu
1 links
arXiv (Cornell University)
Advanced Graph Theory Research
preprint

On two problems concerning the geodesic transversal number of graphs

马儇龙, Shi Chen, Tingzeng Wu
preprint en

Abstract

We establish sharp upper and lower bounds on the geodesic transversal number of hypercubes. We also obtain a lower bound on the geodesic transversal number of Hamming graphs. As applications, we provide negative answers to two open problems concerning the geodesic transversal number.

arXiv (Cornell University)
Advanced Graph Theory Research
DOIOpen Access PDFOpenAlex
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On two problems concerning the geodesic transversal number of graphs — 马儇龙, Shi Chen, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS