# What is the best approximation and exact algorithm for vertex cover on cubic graphs?

"Best" = best performing in terms of run-time for exact algorithm and approximation ratio for an approximation algorithm.

The best-known algorithm for vertex cover in (general) graphs runs in time $$O(1.2114^n)$$ by Bourgeois, Escoffier, Paschos and van Rooij. You may read their paper and see whether their algorithm can be improved for cubic graphs.
Moreover, the following paper proves a hardness result for an ($$1+\epsilon$$) approximation algorithm for vertex cover in cubic graphs.