Author

Xiao-Pan Lian

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Preprint Sep 2026

Weak rainbow saturation numbers of paths, stars and cycles

An edge-colored graph is \emph{rainbow} if all of its edges receive distinct colors. For a fixed graph $H$, an edge-colored graph $F$ is called weakly $H$-rainbow saturated if there exists an ordering $e_1,e_2,\ldots,e_{|E(\bar{F})|}$ of $E(\bar{F})$ such that, for any edge coloring $c$ of $E(\bar{F})$ with $c(e_i)\neq...

Jia-Wen Bo, Xiao-Pan Lian, Jia-Ning Liu · 0 citations

Preprint Aug 2026

An improved finite bound for oriented trees in tournaments

Sumner's universal tournament conjecture asserts that every tournament on $2n-2$ vertices contains every oriented tree on $n$ vertices. Let $f(n)$ be the least integer $N$ such that every tournament on $N$ vertices contains every oriented tree on $n$ vertices. Havet and Thomass\'e proved that $f(n)\le \lceil(7n-5)/2\rc...

Jiangdong Ai, Xiao-Pan Lian · 1 citation