Abstract
We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 345-385 |
| Number of pages | 41 |
| Journal | Algebra Universalis |
| Volume | 49 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2003 |
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Keywords
- Chessboard complex
- Matching complex
- Simplicial complex
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Topology of matching, chessboard, and general bounded degree graph complexes. / Galloway, Michelle L.
In: Algebra Universalis, Vol. 49, No. 4, 2003, p. 345-385.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Topology of matching, chessboard, and general bounded degree graph complexes
AU - Galloway, Michelle L
PY - 2003
Y1 - 2003
N2 - We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.
AB - We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.
KW - Chessboard complex
KW - Matching complex
KW - Simplicial complex
UR - http://www.scopus.com/inward/record.url?scp=0142138127&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0142138127&partnerID=8YFLogxK
U2 - 10.1007/s00012-003-1825-1
DO - 10.1007/s00012-003-1825-1
M3 - Article
VL - 49
SP - 345
EP - 385
JO - Algebra Universalis
JF - Algebra Universalis
SN - 0002-5240
IS - 4
ER -