I was wondering that since (5,5,5,5,4,4,4,4,4,4,4,4,4,4) can be split into a first set (5,5,4,4,4,4,4) and 2nd set (5,5,4,4,4,4,4). It satisfies the condition that the degrees of the first set = degrees of 2nd set, but i still cant draw a bipartite graph with this. So my general question is that if a graph is bipartite then the sum of degrees in one vertex set = sum of degrees in the other vertex set. But the reverse is not true ?
If the reverse is not true, is there a method to know if you can construct a bi partite graph from the degree sequence without actually trying to draw it out ?