Author

Qiwen Guo

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Preprint Oct 2026

Sharp lower bounds for bisections of graphs with bounded maximum degree

A bisection of a graph is a partition of its vertex set into two parts whose sizes differ by at most one. We prove that every graph with $m$ edges and maximum degree at most $k$ has a bisection of size at least $\frac{k+1}{2k}m$ when $k$ is odd, and at least $\frac{k+2}{2(k+1)}m$ when $k$ is even. Both bounds are sharp...

Qi-Wen Guo, G. Gutin · 0 citations

Preprint Aug 2026

Bounds on Odd and Odd-Even Induced Subgraphs

Let $G$ be an $n$-vertex graph and let $\ell:V(G)\to\mathbb{F}_2$ prescribe degree parities. A set $S\subseteq V(G)$ is $\ell$-admissible if every $v\in S$ has degree congruent to $\ell(v)$ modulo $2$ in $G[S]$. Let $h_\ell(G)$ be the maximum order of an $\ell$-admissible set, set $f_{\mathrm{oe}}(G):=\min_\ell h_\ell(...

Qiwen Guo, G. Gutin, Yi-Ming Hao et al. · 0 citations