"Sphere Representations, Stacked Polytopes, and the Colin de Verdière N" by Lon Mitchell and Lynne Yengulalp
 

Document Type

Article

Publication Date

2016

Publication Source

The Electronic Journal of Combinatorics

Abstract

We prove that a k-tree can be viewed as a subgraph of a special type of (k + 1)- tree that corresponds to a stacked polytope and that these “stacked” (k + 1)-trees admit representations by orthogonal spheres in R k+1. As a result, we derive lower bounds for Colin de Verdi`ere’s µ of complements of partial k-trees and prove that µ(G) + µ(G) > |G| − 2 for all chordal G.

Inclusive pages

1-11

ISBN/ISSN

1077-8926

Document Version

Published Version

Comments

This document is provided for download in compliance with the publisher's policy for self-archiving. Permission documentation is on file.

Publisher

Electronic Journal of Combinatorics

Volume

23

Issue

1

Peer Reviewed

yes


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