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