Geodesic
Relaxations of Ore's condition on cycles
The electronic journal of combinatorics, Tome 13 (2006)
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A simple, undirected $2$-connected graph $G$ of order $n$ belongs to class ${\cal O}(n$,$\varphi)$, $\varphi\geq0$, if $\sigma_{2}=n-\varphi.$ It is well known (Ore's theorem) that $G$ is hamiltonian if $\varphi= 0$, in which case the $2$-connectedness hypothesis is implied. In this paper we provide a method for studying this class of graphs. As an application we give a full characterization of graphs $G$ in ${\cal O}(n$,$\varphi)$, $\varphi\leq3$, in terms of their dual hamiltonian closure.
DOI : 10.37236/1086
Classification : 05C45
Mots-clés : Hamiltonian, characterization 
@article{10_37236_1086,
     author = {Ahmed Ainouche},
     title = {Relaxations of {Ore's} condition on cycles},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1086},
     zbl = {1096.05031},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1086/}
}
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Ahmed Ainouche. Relaxations of Ore's condition on cycles. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1086

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