Jun Yan

collaborators

3 papers

math.CO2025

Asymmetric Ramsey numbers of trees

Jun Yan

Let $n \geq ν$ , let $T$ be an $n$ -vertex tree with bipartition class sizes $t_{1} \geq t_{2}$ , and let $S$ be a $ν$ -vertex tree with bipartition class sizes $τ_{1} \geq τ_{2}$ . Using four natur…

math.CO2025

Spanning trees with large maximum degrees

Jun Yan

The celebrated result of Komlós, Sárközy, and Szemerédi states that for any $ε > 0$ , there exists $0 < c < 1$ , such that for all sufficiently large $n$ , every $n$ -vertex graph…

math.CO2025

Ramsey numbers of trees

Richard Montgomery, Matías Pavez-Signé, Jun Yan

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