## Zero Forcing Sets in H-matchable Graphs

- Nov. 20, 2020
- 3:30 p.m.

## Abstract

In this talk, a graph G = (V(G), E(G)) has no isolated vertices and is finite, simple, and undirected. Fix a non-trivial connected graph H. A perfect H-matching of a graph G is a set {H1, ...,Hn} of vertex-induced subgraphs of G (i.e., all G[V(Hi )] = Hi ) where {V(H1), ..., V(Hn)} partitions V(G) and each subgraph Hi = H. Two perfect H-matchings of G are equal iff they are equal as sets of graphs. A perfect matching of G is then a perfect P2-matching of G. We say that G is H-matchable (matchable) iff G has a perfect H-matching (perfect matching). If G has a perfect H-matching, then |V(G)| = 0 mod |V(H)|. We assume this throughout the talk.