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A graph $H$ is called common and respectively, strongly common if the number of monochromatic copies of $H$ in a 2-edge-coloring $\phi$ of a large clique is asymptotically minimised by the random coloring with an equal proportion of each color and respectively, by the random coloring with the same proportion of each color as in $\phi$.
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L. Lovász, · 2011
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Non-three-colourable common graphs exist,
H. Hatami, J. Hladký, D. Král’, S. Norine, and A. A. Razborov, · 2012
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N. Behague, N. Morrison, and J. A. Noel,
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Towards characterizing locally common graphs,
R. Hancock, D. Král’, M. Krnc and J. Volec,
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On tripartite common graphs,
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J. S. Kim and J. Lee,
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Non-bipartite
D. Král’, J. A. Noel, S. Norin, J. Volec, and F. Wei, · 2022
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