Sebastian M. Cioaba, Vishal Gupta: A lower bound for the smallest eigenvalue of a graph and an application to the associahedron graph, 393-404

Abstract:

In this paper, we obtain a lower bound for the smallest eigenvalue of a regular graph containing many copies of a smaller fixed subgraph. This generalizes a result of Aharoni, Alon, and Berger in which the subgraph is a triangle. We apply our results to obtain a lower bound on the smallest eigenvalue of the associahedron graph, and we prove that this bound gives the correct order of magnitude of this eigenvalue. We also survey what is known regarding the second-largest eigenvalue of the associahedron graph.

Key Words: Associahedron graph, smallest eigenvalue, second largest eigenvalue, triangulation, mixing time.

2010 Mathematics Subject Classification: Primary 05C50; Secondary 05C81.

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