The maximum size of a nonhamiltonian-connected graph with given order and minimum degree
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909317388566528 |
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| author | Zhang, Leilei |
| author_facet | Zhang, Leilei |
| contents | 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 $k$-connected nonhamiltonian-connected graph with a given order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximum size of a nonhamiltonian-connected graph with given order and minimum degree Zhang, Leilei Combinatorics 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 $k$-connected nonhamiltonian-connected graph with a given order. |
| title | The maximum size of a nonhamiltonian-connected graph with given order and minimum degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.10255 |