1). In a league with two divisions of 13 teams each, determine whether it is possible to schedule a season with each team playing 9 games against teams in its division and 4 games against teams in other division

2).Let G be the graph with vertex set {1, ., 15} and where i and j are adjacent if and only if their greatest common factor exceeds 1.How many components are in G and what is the length of the longest path in G?

3). For k2, prove that a k-regular bipartite graph has no cut edge.