MANIFOLD MATCHING COMPLEXES
The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper, we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or with...
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| Published in: | Mathematika Vol. 66; no. 4; pp. 973 - 1002 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01-10-2020
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper, we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or without boundary. Except in dimension two, all of these manifolds are spheres or balls. |
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| Bibliography: | This work was done in part at the 2018 Graduate Research Workshop in Combinatorics. The workshop was partially funded by NSF grants 1603823, 1604773, and 1604458, “Collaborative Research: Rocky Mountain ‐ Great Plains Graduate Research Workshops in Combinatorics,” NSA grant H98230‐18‐1‐0017, “The 2018 and 2019 Rocky Mountain ‐ Great Plains Graduate Research Workshops in Combinatorics,” Simons Foundation Collaboration Grants #316262 and #426971, and grants from the Combinatorics Foundation and the Institute for Mathematics and its Applications. Margaret Bayer also received support from the University of Kansas General Research Fund. Bennet Goeckner also received support from an AMS‐Simons travel grant. Marija Jelić Milutinović also received support from Grant #174034 of the Ministry of Education, Science and Technological Development of Serbia. |
| ISSN: | 0025-5793 2041-7942 |
| DOI: | 10.1112/mtk.12049 |