M edges. A simple graph is an undirected graph that has no self-loops and no more than one edge between any two different vertices. Initially, each edge is colored white. Each round you can pick a white edge and paint it in red. You are not allowed to generate an odd-length cycle that consists only of red edges. What's the maximum number of edges that can be painted to red?
You are given a simple graph with mathbf{N} N vertices and mathbf{M} M edges. A simple graph is an undirected graph that has no self-loops (edges connected at both ends to the same vertex) and no more than one edge between any two different vertices. Initially, each edge is colored white. Each round you can pick a white edge and paint it in red. You are not allowed to generate an odd-length cycle that consists only of red edges. What's the maximum number of edges that can be painted to red?
（图片来源网络，侵删）
