The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. The perfect matching complex is the subcomplex generated by perfect matchings (independent sets of edges that cover all vertices of the graph). This talk presents a number of recent results on the topology of matching complexes and perfect matching complexes of certain graphs, including polygonal line tilings and honeycomb graphs.
Matching Complexes of Graphs
Margaret Bayer, University of KansasAuthors: Margaret Bayer, Marija Jeli'c Milutinovi'c, and Julianne Vega
2022 AWM Research Symposium
Advances in Combinatorics