$4.$ Consider the following problem:

Definition: An Eulerian cycle of an undirected graph is a path that starts

and ends at the same vertex and contains each edge of the graph exactly once.

Problem: Given a connected undirected graph, to decide whether it contains

an Eulerian cycle.

Is this problem in P$?$ If yes, give a polynomial time algorithm.

Is this problem NP$-$complete? If yes, prove your claim.