MORE NON-BIPARTITE FORCING PAIRS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113680" target="_blank" >RIV/00216224:14330/19:00113680 - isvavai.cz</a>
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
MORE NON-BIPARTITE FORCING PAIRS
Original language description
We study pairs of graphs (H-1, H-2) such that every graph with the densities of H-1 and H-2 close to the densities of H-1 and H-2 in a random graph is quasirandom; such pairs (H-1, H-2) are called forcing. Non-bipartite forcing pairs were first discovered by Conlon, Han, Person and Schacht [Weak quasi-randomness for uniform hypergraphs, Random Structures Algorithms 40 (2012), no. 1, 1-38]: they showed that (K-t, F) is forcing where F is the graph that arises from K-t by iteratively doubling its vertices and edges in a prescribed way t times. Reiher and Schacht [Forcing quasirandomness with triangles, Forum of Mathematics, Sigma. Vol. 7, 2019] strengthened this result for t = 3 by proving that two doublings suffice and asked for the minimum number of doublings needed for t > 3. We show that [t + 1)/2] doublings always suffice.
Czech name
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Czech description
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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

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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