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Smith, J.P. 
ORCID: 0000-0002-4209-1604,
2019.
The poset of graphs ordered by induced containment.
Journal of Combinatorial Theory, Series A, 168, pp. 348-373.
ISSN 0097-3165
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Abstract
We study the poset G of all unlabelled graphs with H ≤ G if H occurs as an induced subgraph in G. We present some general results on the Möbius function of intervals of G and some results for specific classes of graphs. This includes a case where the Möbius function is given by the Catalan numbers, which we prove using discrete Morse theory, and another case where it equals the Fibonacci numbers, therefore showing that the Möbius function is unbounded. A classification of the disconnected intervals of G is presented, which gives a large class of non-shellable intervals. We also present several conjectures on the structure of G.
| Item Type: | Journal article | ||||||||
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| Publication Title: | Journal of Combinatorial Theory, Series A | ||||||||
| Creators: | Smith, J.P. | ||||||||
| Publisher: | Elsevier | ||||||||
| Date: | November 2019 | ||||||||
| Volume: | 168 | ||||||||
| ISSN: | 0097-3165 | ||||||||
| Identifiers: |
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| Divisions: | Schools > School of Science and Technology | ||||||||
| Record created by: | Linda Sullivan | ||||||||
| Date Added: | 20 Apr 2021 15:53 | ||||||||
| Last Modified: | 14 Jan 2022 11:34 | ||||||||
| URI: | https://irep.ntu.ac.uk/id/eprint/42724 |
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