Geodesic
An existence theorem on Hamiltonian $(g,f)$-factors in networks
Zhou, Sizhong 1
1 School of Science, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, P. R. China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 1, p. 1-7.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Let $a,b$, and $r$ be nonnegative integers with $\max\{3,r+1\}\leq a$, let $G$ be a graph of order $n$, and let $g$ and $f$ be two integer-valued functions defined on $V(G)$ with $\max\{3,r+1\}\leq a\leq g(x)$ for any $x\in V(G)$. In this article, it is proved that if $n\geq\frac{(a+b-3)(a+b-5)+1}{a-1+r}$ and ${\rm bind}(G)\geq\frac{(a+b-3)(n-1)}{(a-1+r)n-(a+b-3)}$, then $G$ admits a Hamiltonian $(g,f)$-factor.
DOI : 10.22436/jnsa.011.01.01
Classification : 05C70, 05C45
Keywords: Network, graph, binding number

Zhou, Sizhong  1

1 School of Science, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, P. R. China 
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Zhou, Sizhong . An existence theorem on Hamiltonian \((g,f)\)-factors in networks. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 1, p. 1-7. doi : 10.22436/jnsa.011.01.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.01.01/

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