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PreprintCC BY 4.0arXiv

On two problems concerning the geodesic transversal number of graphs

  • Shi Chen
  • Xuanlong Ma
  • Tingzeng Wu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026problems,
  title = {{On two problems concerning the geodesic transversal number of graphs}},
  author = {Shi Chen and Xuanlong Ma and Tingzeng Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39298},
  eprint = {2610.39298},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39298},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On two problems concerning the geodesic transversal number of graphs
AU  - Shi Chen
AU  - Xuanlong Ma
AU  - Tingzeng Wu
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39298
UR  - https://arxiv.org/abs/2610.39298
AB  - 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.
ER  -