The Relation Between Hamiltonian and 1-Tough Properties of the Cartesian Product Graphs

Louis Kao*, Chih wen Weng

*此作品的通信作者

研究成果: Article同行評審

摘要

The relation between Hamiltonicity and toughness of a graph is a long standing research problem. The paper studies the Hamiltonicity of the Cartesian product graph G1□ G2 of graphs G1 and G2 satisfying that G1 is traceable and G2 is connected with a path factor. Let Pn be the path of order n and H be a connected bipartite graph. With certain requirements of n, we show that the following three statements are equivalent: (i) Pn□ H is Hamiltonian; (ii) Pn□ H is 1-tough; and (iii) H has a path factor.

原文English
頁(從 - 到)933–943
頁數11
期刊Graphs and Combinatorics
37
發行號3
DOIs
出版狀態Published - 5月 2021

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