Is there any relation between average degree of a graph and chromatic number?
Like if an average degree for a graph is 3.4. Can we say that the graph is not 2-colorable? for Number of edges = 17 and vertices are 10.
So my question is can we do prove of this using handshaking lemma min.degree <= 2E/V <= max. degree ? i.e. if my average degree comes say x then chromatic number is greater than or equal to x ?