Year: 2026
Type: preprint
Abstract: Let $G$ be a simple graph of order $n$ satisfying the following Ore-type condition: For any two nonadjacent vertices $x$ and $y$ of $G$, $d_G(x)+d_G(y)\geq n+k-2$, where $1\leq k\leq n-1$, $kn$ is even and $d_G(x)$ is the degree of $x$ in $G$. It is well known that $G$ has a $k$-factor for $k=1$ or $2$. Lu and Ning (J. Graph Theory, 94(2020), 307-319) proved that if $k\geq n/2$, then $G$ has a $k$-factor. In this paper, we show that $G$ has a $k$-factor for any $1\leq k\leq n-1$.
Source: arXiv (Cornell University)
Authors: Lai, Jingchao, Yan, Weigen
Institution: Jimei University
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204230255
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