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- W2768496138 abstract "Let $G$ be a graph on $n$ vertices with degree sequence $delta=d_1le d_2le...le d_n$. Let $c$ be the circumference - the order of a longest cycle and $p$ the order of a longest path in $G$. In 1952, Dirac proved: (i) every graph with $2d_1ge n$ is hamiltonian; (ii) in every 2-connected graph, $cge min{p,2d_1}$. Recently, the bounds $2d_1ge n$ and $cge min{p,2d_1}$ in (i) and (ii) are improved to $2d_deltage n$ and $cge min{p,2d_delta}$, respectively, by Koulakzian, Mosesyan and Nikoghosyan. In this paper we present two new sharp bounds $d_delta+d_{delta+1}ge n$ and $min{2d_{delta+1},d_delta+d_{delta+2}}ge n$ instead of $2d_deltage n$, as well as two new sharp bounds $cge min{p,d_delta+d_{delta+1}}$ and $cge min{p,2d_{delta+1},d_delta+d_{delta+2}}$ instead of $cge min{p,2d_delta}$." @default.
- W2768496138 created "2017-12-04" @default.
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- W2768496138 date "2017-11-11" @default.
- W2768496138 modified "2023-09-27" @default.
- W2768496138 title "Degree Sequences and Long Cycles in Graphs" @default.
- W2768496138 hasPublicationYear "2017" @default.
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