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December 1997 Neighborhood Conditions and $k$-Factors
Tadashi IIDA, Tsuyoshi NISHIMURA
Tokyo J. Math. 20(2): 411-418 (December 1997). DOI: 10.3836/tjm/1270042114

Abstract

Let $k$ be an integer such that $k\geq 2$, and let $G$ be a connected graph of order $n$ such that $n\geq 9k-1-4\sqrt{2(k-1)^2+2}$, $kn$ is even, and the minimum degree is at least $k$. We prove that if $|N_G(u)\cup N_G(v)|\geq\frac{1}{2}(n+k-2)$ for each pair of nonadjacent vertices $u$, $v$ of $G$, then $G$ has a $k$-factor.

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Tadashi IIDA. Tsuyoshi NISHIMURA. "Neighborhood Conditions and $k$-Factors." Tokyo J. Math. 20 (2) 411 - 418, December 1997. https://doi.org/10.3836/tjm/1270042114

Information

Published: December 1997
First available in Project Euclid: 31 March 2010

zbMATH: 0897.05064
MathSciNet: MR1489474
Digital Object Identifier: 10.3836/tjm/1270042114

Rights: Copyright © 1997 Publication Committee for the Tokyo Journal of Mathematics

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Vol.20 • No. 2 • December 1997
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