Suppose G is a (10,23) graph and is also bipartite. Determine all possible degree sequences. I can't seem to come up with a solution. There just seem to be too many possibilities. I know that if the graph is bipartite we need to come up with a partition of the vertices such that the sum of the degrees in each partition is 23. But then the issue arises such that G could be disconnected.
Any suggestions or solutions?
The key question is how many edges there are in the complete bipartite graph $K_{i, 10-i}$. Then subtract $23$ to see how many of those edges are missing.