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

2021/06/02 by Xingzhi Zhan, Zhan, Xingzhi, Leilei Zhang +1
Computer Science · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems #Nanocluster Synthesis and Applications

paper · pdf · doi:10.48550/arxiv.2106.00904

openalex publication_date 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 corresponding problem for nontraceable graphs.

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