For my senior research project at California Polytechnic State University, I studied a class of spanning trees and wrote proofs concerning criterion for their existanceand bounds for how many can be packed into a given graph.

A T2 Tree is a certain type of spanning tree of an almost balanced bipartite graph. In particular, if a bipartite graph G has n vertices in X and n+1 vertices in Y, then a T2 tree T on G is a spanning tree on G such that every vertex of the spanning tree in X is degree 2.

An example T2 tree (blue edges)