Matching Complexes of Outerplanar Graphs
Margaret Bayer, Marija Jeli\'c Milutinovi\'c, Julianne Vega
TL;DR
This paper investigates the topological properties of matching complexes in outerplanar graphs, showing they are either contractible or homotopy equivalent to a wedge of spheres, extending previous results on simpler graph classes.
Contribution
It proves that matching complexes of outerplanar graphs are contractible or homotopy equivalent to wedges of spheres, generalizing known results from trees and polygonal line tilings.
Findings
Matching complexes are either contractible or wedge of spheres.
Extends topological results from trees to outerplanar graphs.
Provides a unified topological characterization of outerplanar graph matchings.
Abstract
An outerplanar graph is a planar graph that has a planar drawing with all vertices on the unbounded face. The matching complex of a graph is the simplicial complex whose faces are subsets of disjoint edges of the graph. In this paper we prove that the matching complexes of outerplanar graphs are contractible or homotopy equivalent to a wedge of spheres. This extends known results about trees and polygonal line tilings.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Graph Theory and Algorithms · Data Management and Algorithms