3 papers
math.CO2026
An improved polynomial -bound for -free graphs
Kaiyang Lan, Wenlong Zhong
Nguyen~\cite{Nguyen2025} recently proved that every -free graph satisfies . Building on his framework, we introduce two refinements, namely a s…
math.CO2026
On a problem of Sivaraman and a problem of Gyárfás
Kaiyang Lan, Wenlong Zhong
The \textit{girth} of a graph , denoted , is the length of a shortest cycle in . If contains no cycle, we define . Sivaraman (2020) a…
math.CO2026
On two conjectures of Hoà ng
Hongzhang Chen, Kaiyang Lan, Wenlong Zhong
A graph is said to be perfectly divisible if for every induced subgraph of with at least one edge, the vertex set can be partitioned into two sets such th…