Spectral radius and Hamiltonian properties of graphs, II
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arXiv
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| Format: | Preprint |
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2016
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| _version_ | 1866908600207671296 |
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| author | Ge, Jun Ning, Bo |
| author_facet | Ge, Jun Ning, Bo |
| contents | In this paper, we first present spectral conditions for the existence of $C_{n-1}$ in graphs (2-connected graphs) of order $n$, which are motivated by a conjecture of Erdős. Then we prove spectral conditions for the existence of Hamilton cycles in balanced bipartite graphs. This result presents a spectral analog of Moon-Moser's theorem on Hamilton cycles in balanced bipartite graphs, and extends a previous theorem due to Li and the second author for $n$ sufficiently large. We conclude this paper with two problems on tight spectral conditions for the existence of long cycles of given lengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1606_08530 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Spectral radius and Hamiltonian properties of graphs, II Ge, Jun Ning, Bo Combinatorics 05C50, 15A18, 05C38 In this paper, we first present spectral conditions for the existence of $C_{n-1}$ in graphs (2-connected graphs) of order $n$, which are motivated by a conjecture of Erdős. Then we prove spectral conditions for the existence of Hamilton cycles in balanced bipartite graphs. This result presents a spectral analog of Moon-Moser's theorem on Hamilton cycles in balanced bipartite graphs, and extends a previous theorem due to Li and the second author for $n$ sufficiently large. We conclude this paper with two problems on tight spectral conditions for the existence of long cycles of given lengths. |
| title | Spectral radius and Hamiltonian properties of graphs, II |
| topic | Combinatorics 05C50, 15A18, 05C38 |
| url | https://arxiv.org/abs/1606.08530 |