Work

On the Minimum Number of Hamilton Cycles in Hamiltonian Threshold Graphs: A Simple Proof

Year: 2026

Type: article

Abstract: A graph is called a threshold graph if it is induced-$\{P_4,C_4,2K_2\}$ free. In 2020, Qiao and Zhan [J. Graph Theory 93 (2020) 222--229] determined the minimum number of Hamilton cycles in a Hamiltonian threshold graph and characterized the extremal graphs attaining this minimum. We show that every Hamiltonian threshold graph contains a special spanning subgraph, from which their two results follow directly.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/15076

Authors: Chengli Li, Feng Liu

Institutions: South China Normal University, Fuzhou University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality

Awards: G1609915050, G4716027175, G486494320, G7160286548, G7270659173