Broken circuit complexes of series-parallel networks

Autor(en): Van Le, Dinh
Stichwörter: Mathematics; MATROIDS
Erscheinungsdatum: 2016
Herausgeber: ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Journal: EUROPEAN JOURNAL OF COMBINATORICS
Volumen: 51
Startseite: 12
Seitenende: 36
Zusammenfassung: 
Let (h(0), h(1), ... , h(s)) with h(s) not equal 0 be the h-vector of the broken circuit complex of a series-parallel network M. Let G be a graph whose cycle matroid is M. We give a formula for the difference h(s-1) - h(1) in terms of an ear decomposition of G. A number of applications of this formula are provided, including several bounds for h(s-1) - h(1), a characterization of outerplanar graphs, and a solution to a conjecture on A-graphs posed by Fenton. We also prove that h(s-2) >= h(2) when s >= 4. (C) 2015 Elsevier Ltd. All rights reserved.
ISSN: 01956698
DOI: 10.1016/j.ejc.2015.04.009

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