On tripartite common graphs
Typ dokumentu
článek v časopisejournal article
Peer-reviewed
acceptedVersion
Autor
Grzesik A.
Lee J.
Lidický B.
Volec J.
Práva
openAccessMetadata
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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.
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Kolekce
- Publikační činnost ČVUT [1323]