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Complexes of directed trees and independence complexes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2007 (English)In: FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics, 2007Conference paper, Published paper (Refereed)
Abstract [en]

The theory of complexes of directed trees was initiated by Kozlov to answer a question by Stanley, and later on, results from the theory were used by Babson and Kozlov in their proof of the Lovász conjecture. We develop the theory and prove that complexes on directed acyclic graphs are shellable. A related concept is that of independence complexes: construct a simplicial complex on the vertex set of a graph, by including each independent set of vertices as a simplex. Two theorems used for breaking and gluing such complexes are proved and applied to generalize results by Kozlov. A fruitful restriction is anti-Rips complexes: a subset P of a metric space is the vertex set of the complex, and we include as a simplex each subset of P with no pair of points within distance r. For any finite subset P of R the homotopy type of the anti-Rips complex is determined.

Place, publisher, year, edition, pages
2007.
Keyword [en]
Anti-Rips complexes, Complexes of directed trees, Graph complexes, Independence complexes
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-154657Scopus ID: 2-s2.0-84860718796OAI: oai:DiVA.org:kth-154657DiVA: diva2:758656
Conference
19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, 2 July 2007 through 6 July 2007, Tianjin, China
Note

QC 20141028

Available from: 2014-10-28 Created: 2014-10-27 Last updated: 2014-10-28Bibliographically approved

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