给定阶数和最小阶数的非哈密顿连接图的最大尺寸

arXiv - MATH - Combinatorics Pub Date : 2024-09-16 DOI:arxiv-2409.10255

Leilei Zhang

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引用次数: 0

摘要

在本文中，我们确定了具有规定阶数和最小度数的非哈密顿连接图的最大尺寸。我们还描述了达到这个最大尺寸的极端图的特征。这项工作概括了之前由 Ore [ J. Math. Pures Appl.作为我们主要结果的推论，我们确定了具有给定阶的 $k$ 连接非哈密顿连接图的最大尺寸。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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arXiv - MATH - Combinatorics

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