Jun Yan

collaborators

4 papers

math.CO2026

More Shattering News

Attila Sali, Jun Yan

An ordered variant of the well-known set theory concept of shattering was introduced by Anstee, RÃ³nyai, and Sali. In this paper, we prove several new results related to order shat…

math.CO2025

Asymmetric Ramsey numbers of trees

Jun Yan

Let $n \geq I^½$ , let $T$ be an $n$ -vertex tree with bipartition class sizes $t_{1} \geq t_{2}$ , and let $S$ be a $I^½$ -vertex tree with bipartition class sizes $I ¨ _{1} \geq I ¨ _{2}$ . Using four n…

math.CO2025

Spanning trees with large maximum degrees

Jun Yan

The celebrated result of KomlÃ³s, SÃ¡rkÃ¶zy, and SzemerÃ©di states that for any $ε > 0$ , there exists $0 < c < 1$ , such that for all sufficiently large $n$ , every $n$ -vertex gr…

math.CO2025

Ramsey numbers of trees

We show that there exists a constant $c > 0$ such that every $n$ -vertex tree $T$ with $I^ (T) \leq c n$ has Ramsey number $R (T) = max {t_{1} + 2 t_{2}, 2 t_{1}} - 1$ , where $t_{1} \geq t_{2}$ are the sizes…