On tripartite common graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00361762" target="_blank" >RIV/68407700:21340/22:00361762 - isvavai.cz</a>
Result on the web
<a href="http://hdl.handle.net/10467/105477" target="_blank" >http://hdl.handle.net/10467/105477</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0963548322000074" target="_blank" >10.1017/S0963548322000074</a>

Result language
angličtina
Original language name
On tripartite common graphs
Original language description
This work provides several new classes of tripartite common graphs. A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph K-n is asymptotically minimised by the random colouring. Burr and Rosta, extending a famous conjecture of Erdős, conjectured that every graph is common. The conjectures of Era's and of Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. The first new class are the so-called triangle trees, which generalises two theorems by Sidorenko and answers a question of Jagger, Šťovíček, and Thomason from 1996. We also prove that, somewhat surprisingly, given any tree T, there exists a triangle tree such that the graph obtained by adding T as a pendant tree is still common. Furthermore, we show that adding arbitrarily many apex vertices to any connected bipartite graph on at most 5 vertices yields a common graph.
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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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