Calculating the [domination number](https://en.wikipedia.org/wiki/Dominating_set) is an NP-Hard problem. Does it remain NP-Hard if we restrict it to non-bipartite graphs?



Is the domination number NP for non-bipartite graphs?
The general case of the domination number problem reduces to the non-bipartite case. Given a (possibly bipartite graph) $G$, create new graph $G'$ consisting of an copy of $G$ and a disjoint copy of $K\_3$. The domination number of the new (non-bipartite) graph $G'$ is exactly one more than that of the original graph $G$. So computing the domination number of the new graph $G'$ is exactly as hard as computing that of the original graph $G$.


