English

The maximum size of a nonhamiltonian-connected graph with given order and minimum degree

Combinatorics 2024-09-17 v1

Abstract

In this paper, we determine the maximum size of a nonhamiltonian-connected graph with prescribed order and minimum degree. We also characterize the extremal graphs that attain this maximum size. This work generalizes a previous result obtained by Ore [ J. Math. Pures Appl. 42 (1963) 21-27] and further extends a theorem proved by Ho, Lin, Tan, Hsu, and Hsu [Appl. Math. Lett. 23 (2010) 26-29]. As a corollary of our main result, we determine the maximum size of a kk-connected nonhamiltonian-connected graph with a given order.

Keywords

Cite

@article{arxiv.2409.10255,
  title  = {The maximum size of a nonhamiltonian-connected graph with given order and minimum degree},
  author = {Leilei Zhang},
  journal= {arXiv preprint arXiv:2409.10255},
  year   = {2024}
}

Comments

10 pages. arXiv admin note: text overlap with arXiv:2107.01416