Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Degree Condition for Graphs Having All $(a,b)$-Parity Factors   Let $a$ and $b$ be positive integers such that $a\leq b$ and $a\equiv b\pmod
2$. We say that $G$ has all $(a, b)$-parity factors if $G$ has an $h$-factor
for every function $h: V(G) \rightarrow \{a,a+2,\ldots,b-2,b\}$ with $b|V(G)|$
even and $h(v)\equiv b\pmod 2$ for all $v\in V(G)$. In this paper, we prove
that every graph $G$ with $n\geq 3(b+1)(a+b)$ vertices has all $(a,b)$-parity
factors if $\delta(G)\geq (b^2-b)/a$, and for any two nonadjacent vertices $u,v
\in V(G)$, $\max\{d_G(u),d_G(v)\}\geq \frac{bn}{a+b}$. Moreover, we show that
this result is best possible in some sense.

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The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org