Let K_4 be the complete graph on four vertices. Complete-graph K_4 conjecture. For every m≥4, H^1,2m-1_ A_m(K_4)=Z_m^4 oplusZ_2 oplusZ^2. The paper reports verification for m≤14, but does not establish the stated range in general.

Cohomology conjecture for the complete graph $K_4$

Let $K_4$ be the complete graph on four vertices. Complete-graph $K_4$ conjecture. For every $m\geq4$ ,

H^{1,2m-1}_{{\mathcal A}_m}(K_4)=\mathbb{Z}_m^4\oplus\mathbb{Z}_2\oplus\mathbb{Z}^2.

The paper reports verification for $m\leq14$ , but does not establish the stated range in general.

References

Milena D. Pabiniak, Jozef H. Przytycki and Radmila Sazdanovic, “On the first group of the chromatic cohomology of graphs”, arXiv:math/0607326 (2006).

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