Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs
A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that eve...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2016-11-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1897 |
| Summary: | A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost obtain a complete solution to this problem, leaving H = K1 ∪ P4 as the only open case. |
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| ISSN: | 2083-5892 |