For every m ≥ 2, the wheel graph W_{2m+1} is homologous to an explicit linear combination of 2^{m-2} graphs with only 3- and 4-valent vertices in the Kontsevich graph complex GC_d.
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Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture
For every m ≥ 2, the wheel graph W_{2m+1} is homologous to an explicit linear combination of 2^{m-2} graphs with only 3- and 4-valent vertices in the Kontsevich graph complex GC_d.