Fixed Simplex Property for Retractable Complexes
<p>Abstract</p> <p>Retractable complexes are defined in this paper. It is proved that they have the fixed simplex property for simplicial maps. This implies the theorem of Wallace and the theorem of Rival and Nowakowski for finite trees: every simplicial map transforming vertices o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/303640 |
| _version_ | 1818731428438867968 |
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| author | Zapart Anna Idzik Adam |
| author_facet | Zapart Anna Idzik Adam |
| author_sort | Zapart Anna |
| collection | DOAJ |
| description | <p>Abstract</p> <p>Retractable complexes are defined in this paper. It is proved that they have the fixed simplex property for simplicial maps. This implies the theorem of Wallace and the theorem of Rival and Nowakowski for finite trees: every simplicial map transforming vertices of a tree into itself has a fixed vertex or a fixed edge. This also implies the Hell and Nešetřil theorem: any endomorphism of a dismantlable graph fixes some clique. Properties of recursively contractible complexes are examined.</p> |
| first_indexed | 2024-12-17T23:17:31Z |
| format | Article |
| id | doaj.art-570f3b58d788447b8e2e8048ca38ed14 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-17T23:17:31Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-570f3b58d788447b8e2e8048ca38ed142022-12-21T21:28:59ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101303640Fixed Simplex Property for Retractable ComplexesZapart AnnaIdzik Adam<p>Abstract</p> <p>Retractable complexes are defined in this paper. It is proved that they have the fixed simplex property for simplicial maps. This implies the theorem of Wallace and the theorem of Rival and Nowakowski for finite trees: every simplicial map transforming vertices of a tree into itself has a fixed vertex or a fixed edge. This also implies the Hell and Nešetřil theorem: any endomorphism of a dismantlable graph fixes some clique. Properties of recursively contractible complexes are examined.</p>http://www.fixedpointtheoryandapplications.com/content/2010/303640 |
| spellingShingle | Zapart Anna Idzik Adam Fixed Simplex Property for Retractable Complexes Fixed Point Theory and Applications |
| title | Fixed Simplex Property for Retractable Complexes |
| title_full | Fixed Simplex Property for Retractable Complexes |
| title_fullStr | Fixed Simplex Property for Retractable Complexes |
| title_full_unstemmed | Fixed Simplex Property for Retractable Complexes |
| title_short | Fixed Simplex Property for Retractable Complexes |
| title_sort | fixed simplex property for retractable complexes |
| url | http://www.fixedpointtheoryandapplications.com/content/2010/303640 |
| work_keys_str_mv | AT zapartanna fixedsimplexpropertyforretractablecomplexes AT idzikadam fixedsimplexpropertyforretractablecomplexes |