Independence Complexes of Well-Covered Circulant Graphs
| Autor: | Kevin N. Vander Meulen, Adam Van Tuyl, Jonathan Earl |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Mathematics::Commutative Algebra Well-covered graph General Mathematics 010102 general mathematics 0102 computer and information sciences Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Graph Vertex (geometry) Combinatorics Circulant graph 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics 05C75 05E45 13F55 Combinatorics (math.CO) 0101 mathematics Circulant matrix Mathematics |
| Zdroj: | Experimental Mathematics. 25:441-451 |
| ISSN: | 1944-950X 1058-6458 |
| DOI: | 10.1080/10586458.2015.1091753 |
| Popis: | We study the independence complexes of families of well-covered circulant graphs discovered by Boros-Gurvich-Milani\v{c}, Brown-Hoshino, and Moussi. Because these graphs are well-covered, their independence complexes are pure simplicial complexes. We determine when these pure complexes have extra combinatorial (e.g. vertex decomposable, shellable) or topological (e.g. Cohen-Macaulay, Buchsbaum) structure. We also provide a table of all well-covered circulant graphs on 16 or less vertices, and for each such graph, determine if it is vertex decomposable, shellable, Cohen-Macaulay, and/or Buchsbaum. A highlight of this search is an example of a graph whose independence complex is shellable but not vertex decomposable. Comment: 18 pages |
| Databáze: | OpenAIRE |
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