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On tripartite common graphs
Bibliographic description
| title: | On tripartite common graphs |
| author: | Grzesik Andrzej  , Lee Joonkyung, Lidický Bernard, Volec Jan |
| journal title: | Combinatorics, Probability and Computing |
| volume: | 31 |
| issue: | 5 |
| date of publication : | 2022 |
| pages: | 907-923 |
| ISSN: |
0963-5483 |
| eISSN: |
1469-2163 |
| DOI: | |
| language: | English |
| journal language: | English |
| abstract in English: | A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph Kn 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 Erdős and of Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. Collecting new examples of common graphs had not seen much progress since then, although very recently a few more graphs were verified to be common by the flag algebra method or the recent progress on Sidorenko’s conjecture. Our contribution here is to provide several new classes of tripartite common graphs. The first example is the class of 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. |
| keywords in English: | Sidorenko’s conjecture, common graphs, triangle-tree |
| affiliation: | Wydział Matematyki i Informatyki : Instytut Matematyki |
| type: | journal article |
| subtype: | academic paper |
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Except where otherwise noted, this item's license is described as Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
Projekt „Repozytorium otwartego dostępu do dorobku naukowego i dydaktycznego UJ” współfinansowany w ramach poddziałania 2.3.1 „Cyfrowe udostępnianie zasobów nauki” Programu Operacyjnego Polska Cyfrowa z Europejskiego Funduszu Rozwoju Regionalnego i budżetu państwa na podstawie umowy o dofinansowanie nr POPC.02.03.01-00-0030/17-00
