English

Hamiltonicity in connected regular graphs

Combinatorics 2015-08-06 v1

Abstract

In 1980, Jackson proved that every 2-connected kk-regular graph with at most 3k3k vertices is Hamiltonian. This result has been extended in several papers. In this note, we determine the minimum number of vertices in a connected kk-regular graph that is not Hamiltonian, and we also solve the analogous problem for Hamiltonian paths. Further, we characterize the smallest connected kk-regular graphs without a Hamiltonian cycle.

Keywords

Cite

@article{arxiv.1204.6457,
  title  = {Hamiltonicity in connected regular graphs},
  author = {Daniel W. Cranston and Suil O},
  journal= {arXiv preprint arXiv:1204.6457},
  year   = {2015}
}

Comments

5 pages

R2 v1 2026-06-21T20:56:14.840Z