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Corpus ID: 235294273

The maximum size of a nonhamiltonian graph with given order and connectivity

@inproceedings{Zhan2021TheMS,
title={The maximum size of a nonhamiltonian graph with given order and connectivity},
author={Xingzhi Zhan and Leilei Zhang},
year={2021}
}

Motivated by work of Erdős, Ota determined the maximum size g(n, k) of a k-connected nonhamiltonian graph of order n in 1995. But for some pairs n, k, the maximum size is not attained by a graph of connectivity k. For example, g(15, 3) = 77 is attained by a unique graph of connectivity 7, not 3. In this paper we obtain more precise information by determining the maximum size of a nonhamiltonian graph of order n and connectivity k, and determining the extremal graphs. Consequently we solve the… Expand

As its name implies, this paper consists of observations on various topics in graph theory that stem from the concept of Hamiltonian cycle. We shall mainly adopt the notation and terminology of… Expand

This note will use the terminology of PÓSA'S paper. Gin) will denote a graph of n vertices and l edges and G(,n)(k) denotes a graph of having v vertices 1 edges and every vertex of which has valency… Expand