Spectral radius and Hamiltonicity of graphs with large minimum degree
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 925-940.

Voir la notice de l'article dans Czech Digital Mathematics Library

Let $G$ be a graph of order $n$ and $\lambda ( G) $ the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in $G$. One of the main results of the paper is the following theorem: \endgraf Let $k\geq 2,$ $n\geq k^{3}+k+4,$ and let $G$ be a graph of order $n$, with minimum degree $\delta (G) \geq k.$ If \[ \lambda ( G) \geq n-k-1, \] then $G$ has a Hamiltonian cycle, unless $G=K_{1}\vee (K_{n-k-1}+K_{k})$ or $G=K_{k}\vee (K_{n-2k}+\bar {K}_{k}).$
DOI : 10.1007/s10587-016-0301-y
Classification : 05C35, 05C50
Mots-clés : Hamiltonian cycle; Hamiltonian path; minimum degree; spectral radius 
@article{10_1007_s10587_016_0301_y,
     author = {Nikiforov, Vladimir},
     title = {Spectral radius and {Hamiltonicity} of graphs with large minimum degree},
     journal = {Czechoslovak Mathematical Journal},
     pages = {925--940},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2016},
     doi = {10.1007/s10587-016-0301-y},
     mrnumber = {3556876},
     zbl = {06644042},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0301-y/}
}
TY  - JOUR
AU  - Nikiforov, Vladimir
TI  - Spectral radius and Hamiltonicity of graphs with large minimum degree
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 925
EP  - 940
VL  - 66
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0301-y/
DO  - 10.1007/s10587-016-0301-y
LA  - en
ID  - 10_1007_s10587_016_0301_y
ER  - 
%0 Journal Article
%A Nikiforov, Vladimir
%T Spectral radius and Hamiltonicity of graphs with large minimum degree
%J Czechoslovak Mathematical Journal
%D 2016
%P 925-940
%V 66
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0301-y/
%R 10.1007/s10587-016-0301-y
%G en
%F 10_1007_s10587_016_0301_y
Nikiforov, Vladimir. Spectral radius and Hamiltonicity of graphs with large minimum degree. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 925-940. doi : 10.1007/s10587-016-0301-y. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0301-y/

Cité par Sources :