Discrete Mathematics and Combinatorics Commons^™

Graph-Theoretic Simplicial Complexes, Hajos-Type Constructions, And K-Matchings, Julianne Vega

Theses and Dissertations--Mathematics

A graph property is monotone if it is closed under the removal of edges and vertices. Given a graph G and a monotone graph property P, one can associate to the pair (G,P) a simplicial complex, which serves as a way to encode graph properties within faces of a topological space. We study these graph-theoretic simplicial complexes using combinatorial and topological approaches as a way to inform our understanding of the graphs and their properties.

In this dissertation, we study two families of simplicial complexes: (1) neighborhood complexes and (2) k-matching complexes. A neighborhood complex is a simplicial …