A Note on Independence Complexes of Chordal Graphs and Dismantling
We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses the properties of tree models of chordal graphs.
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| Published in | The Electronic journal of combinatorics Vol. 24; no. 2 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
02.06.2017
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| Online Access | Get full text |
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| Summary: | We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses the properties of tree models of chordal graphs. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/5571 |