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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…
The optimal -bound for -free graphs
Yidong Zhou, Kaiyang Lan
A \textit{diamond} is a graph obtained from \(K_4\) by removing an edge, and a \textit{dart} is a graph obtained from a diamond by adding a pendant edge to a vertex of degree 3. We…
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…
A non-hereditary Pollyanna class that is not strongly Pollyanna
Hongzhang Chen, Kaiyang Lan
Chudnovsky, Cook, Davies, and Oum introduced the notion of Pollyanna graph classes: a class is Pollyanna if for every -bounded class , the intersectio…
On two conjectures of Hoàng
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…