Non-Bipartite K-Common Graphs

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Authors

KRÁĽ Daniel NOEL Jonathan A NORIN Sergey VOLEC Jan WEI Fan

Year of publication 2022
Type Article in Periodical
Magazine / Source COMBINATORICA
MU Faculty or unit

Faculty of Informatics

Citation
Web http://doi.org/10.1007/s00493-020-4499-9
Doi http://dx.doi.org/10.1007/s00493-020-4499-9
Keywords common graphs; extremal combinatorics; Sidorenko's conjecture
Description A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of Kn is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Štovíček and Thomason [20]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.
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