Tree matchings
Alexander Roberts · Journal of Graph Theory · 2019
Abstract An ‐matching in a bipartite graph is a subset of the edges such that each component of is a tree with at most edges and each vertex in has neighbours in . We give sharp sufficient neighbourhood‐conditions for a bipartite graph to contain an ‐matching. As a special case, we prove a conjecture of Bennett, Bonacina, Galesi, Huynh, Molloy and Wollan.