From the 1 of 6 linked papers with an AI index.
6 papers
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
The paper proves that any graph that does not contain an induced path on six vertices, a dart, or a K4 as an induced subgraph can be colored with at most six colors, improving the…
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 intersecti…
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…
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…