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arXiv · 2409.10255

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

Leilei Zhang
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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 $k$-connected nonhamiltonian-connected graph with a given order.

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Leilei Zhang. 2024-09-16. The maximum size of a nonhamiltonian-connected graph with given order and minimum degree. https://arxiv.org/abs/2409.10255

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