6 papers · 1 filter
A note on the logarithmic exponent of Ramsey number
Kaizhe Chen
In this short note, we point out that the recent lower bounds for off-diagonal Ramsey numbers with fixed , together with the recent proof of the Ajtai--Erdős--Koml…
A One-Third Bound for the Maker--Breaker Degree Game
Kaizhe Chen, Xiaonan Chen, Haotian Yang
Let \(H\) be a finite hypergraph with rank and minimum degree \(d\). In the Maker--Breaker degree game, Maker and Breaker alternately claim previously unclaimed hyperedges of \…
Paths of even length with equal-degree endpoints
Kaizhe Chen, Zhen Liu, Qinghou Zeng
Addressing a question posed by Erdős and Hajnal, Chen and Ma proved that, for all , the complete bipartite graph is the unique graph on vertices with…
On a maximal anti-Ramsey conjecture of Burr, Erdős, Graham, and Sós
Matija Bucic, Kaizhe Chen, Jie Ma
Given a graph , the maximal anti-Ramsey function denotes the minimum integer for which there exists an -vertex graph with at least edges admitting an e…
A problem of Erdős and Hajnal on paths with equal-degree endpoints
Kaizhe Chen, Jie Ma
We address a problem posed by Erdős and Hajnal in 1991, proving that for all , every -vertex graph with at least edges contains two vertices of eq…
On a conjecture of Pach-Spencer-Tóth for graph crossing numbers
Kaizhe Chen, Jie Ma
The crossing number of a graph denotes the minimum number of crossings in any planar drawing of . In this short note, we confirm a long-standing conjecture posed by Pach, Sp…