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math.CO2026
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…
math.CO2025
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…