A Degree Sum Condition on the Order, the Connectivity and the Independence Number for Hamiltonicity
Keyword(s):
In [Graphs Combin. 24 (2008) 469–483], the third author and the fifth author conjectured that if $G$ is a $k$-connected graph such that $\sigma_{k+1}(G) \ge |V(G)|+\kappa(G)+(k-2)(\alpha(G)-1)$, then $G$ contains a Hamilton cycle, where $\sigma_{k+1}(G)$, $\kappa(G)$ and $\alpha(G)$ are the minimum degree sum of $k+1$ independent vertices, the connectivity and the independence number of $G$, respectively. In this paper, we settle this conjecture. The degree sum condition is best possible.
2001 ◽
Vol 82
(1)
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pp. 81-101
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2006 ◽
Vol 96
(2)
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pp. 276-295
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2008 ◽
Vol 24
(5)
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pp. 469-483
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2010 ◽
Vol 26
(2)
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pp. 173-186
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2018 ◽
Vol 10
(05)
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pp. 1850069
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