Does there exist a $10$-vertex graph with degrees $1, 1, 3, 3, 6, 6, 6, 7, 8, 9$? How to tell if there exists a graph given degrees of vertices? Not sure how to go about this one
Is there a graph on $10$ vertices with degrees $1, 1, 3, 3, 6, 6, 6, 7, 8, 9$?

HINT: If there’s a vertex of degree $9$, it’s joined to each of the other vertices. If there’s also a vertex of degree $8$, it’s joined to all but one of the other vertices. Is it then possible to have two vertices of degree $1$?
