Author

Guorong Gao

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Preprint Sep 2026

Sparse Approximate Chromatic Profiles of Triangle-Free Graphs

We prove a sparse version of the four-colour theorem of Brandt and Thomass\'{e}, answering a question of Allen, B\"ottcher, Kohayakawa and Roberts. For every fixed $0<\gamma\le1/10$ and every $p=p(n)\in(0,1]$, asymptotically almost surely every spanning triangle-free $H\subseteq G(n,p)$ with $\delta(H)\ge(1/3+\gamma)pn...

Guo-Rong Gao, Jia-Lin He · 0 citations

Preprint Jul 2026

Tight bound for the skew Hamming set-pair problem

Let $X$ be an alphabet, let $t\geq 0$ and $n\geq t+1$, and let $((a_i,b_i))_{i=1}^{m}$ be an ordered family of word pairs in $X^n$ satisfying $dist(a_i,b_i)\geq t+1$ for every $i$ and $dist(a_i,b_j)\leq t$ whenever $i<j$. We prove the sharp bound $m\leq 2^{t+1}$, thereby resolving a problem posed by Alon, Jin, and Suda...

Guorong Gao, Run-Han Zhao · 0 citations