arXiv subjects

Yuanming Luo

Publications and source records attributed to Yuanming Luo.

3 recordsLinked to original sources

arXiv2026

Reconstruction and Symmetry of Two-Token Graphs

We present a proof of the two-token graph reconstruction conjecture. Every finite simple graph $G,H$ of order at least three, $F_2(G) \cong F_2(H)$ if and only if $G \cong H$. We also classify the automorphism groups of two-token graphs whose connected roots have order at least five. Combining these results, we show that, for connected graphs $G,H$ of order at least five, every isomorphism $ϕ:F_2(G)\to F_2(H)$ admits a factorization $ϕ=η\circσ^{(2)}$, where $σ^{(2)}$ is induced by a graph isomorphism $σ:G\to H$, and $η\in \operatorname{Aut}(F_2(H))$ is a product of twin-cut switches or Cartesian exchanges.

math.CO↗

arXiv2026

Almost Every Graph Is Reconstructible from Its Token Graphs

Let $F_k(G)$ denote the $k$-token graph of a finite graph $G$. The token graph reconstruction conjecture asks whether, for any $1\le k<|V(G)|$, $F_k(G)\cong F_k(H)$ implies $G\cong H$. This paper proves that the conjecture holds for almost every graph.

math.CO↗

arXiv2022

Characterizing Distances Between Points in the Level Sets of a Class of Continuous Functions on a Closed Interval

Given a continuous function $f:[a,b]\to\mathbb{R}$ such that $f(a)=f(b)$, we investigate the set of distances $|x-y|$ where $f(x)=f(y)$. In particular, we show that the only distances this set must contain are ones which evenly divide $[a,b]$. Additionally, we show that it must contain at least one third of the interval $[0,b-a]$. Lastly, we explore some higher dimensional generalizations.

math.CA↗