I have a graph named $G$. degree of each node in $G$ is at most $10$. I need to find an algorithm to determine that this graph has any cycle with length less than $20$ with $O(n)$ .
I think it can solve with any theorem related to $Δ(G)$ and cycle in $G$ (but I'm not sure) .
I search it in google and stackoverflow , but I can't find any solution.