On Betti numbers of flag complexes with forbidden induced subgraphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421440" target="_blank" >RIV/00216208:11320/20:10421440 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=9TSGc2aHvI" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=9TSGc2aHvI</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S030500411900001X" target="_blank" >10.1017/S030500411900001X</a>
Alternative languages
Result language
angličtina
Original language name
On Betti numbers of flag complexes with forbidden induced subgraphs
Original language description
We analyse the asymptotic extremal growth rate of the Betti numbers of clique complexes of graphs on n vertices not containing a fixed forbidden induced subgraph H. In particular, we prove a theorem of the alternative: for any H the growth rate achieves exactly one of five possible exponentials, that is, independent of the field of coefficients, the nth root of the maximal total Betti number over n-vertex graphs with no induced copy of H has a limit, as n tends to infinity, and, ranging over all H, exactly five different limits are attained. For the interesting case where H is the 4-cycle, the above limit is 1, and we prove a superpolynomial upper bound.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ16-01602Y" target="_blank" >GJ16-01602Y: Topological and geometric approaches to classes of permutations and graph properties</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Proceedings of the Cambridge Philosophical Society
ISSN
0305-0041
e-ISSN
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Volume of the periodical
168
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
34
Pages from-to
567-600
UT code for WoS article
000527961800009
EID of the result in the Scopus database
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