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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…
Trisimplicial vertices in (fork, odd parachute)-free graphs
Kaiyang Lan, Feng Liu, Di Wu +1
An {\em odd hole} in a graph is an induced subgraph which is a cycle of odd length at least five. An {\em odd parachute} is a graph obtained from an odd hole by adding a new ed…
Borodin-Kostochka Conjecture holds for odd-hole-free graphs
Rong Chen, Kaiyang Lan, Xinheng Lin +1
The Borodin-Kostochka Conjecture states that for a graph , if , then . In this paper, we prove the Borodin-Kostochka Conjecture holding…