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Elementary Proofs of Commonality of the House Graph and $K_4$ with One Edge Subdivided
A graph $H$ is called common if the number of monochromatic copies of $H$ in a $2$-edge-coloring of a large complete graph is asymptotically minimized by the random coloring with an equal proportion of each color. The house graph and $K_4$ with one edge subdivided once are known to be common by the
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