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Strongly common graphs with odd girth are cycles

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arxiv 2305.10903 v1 pith:JPRBNC3U submitted 2023-05-18 math.CO

Strongly common graphs with odd girth are cycles

classification math.CO
keywords commonstronglycoloringcopiesgirthgraphmonochromaticnumber
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A graph $H$ is called strongly common if for every coloring $\phi$ of $K_n$ with two colors, the number of monochromatic copies of $H$ is at least the number of monochromatic copies of $H$ in a random coloring of $K_n$ with the same density of color classes as $\phi$. In this note we prove that if a graph has odd girth but is not a cycle, then it is not strongly common. This answers a question of Chen and Ma.

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