Conjecture on the fractional chromatic number of odd-wheel squares

About 1 year old · traced to

Let WtW_t be the join of the cycle CtC_t with K1K_1, let χf(G)\chi_f(G) denote the fractional chromatic number of a graph GG, and let W2t+1□2W_{2t+1}^{\Box 2} be the Cartesian square of the odd wheel. Odd-wheel fractional-chromatic-number conjecture.

χf(W2t+1□2)=6t2+7t+32t2+t+1.\chi_f(W_{2t+1}^{\Box 2})=\frac{6t^2+7t+3}{2t^2+t+1}.

The formula is extrapolated from computations of the reduced linear program for small values of tt; its validity for all tt is open.

References

Primary source

Alexander Clow, Hitesh Kumar and Shivaramakrishna Pragada, “Improved Bounds for the Ultimate Independence Ratio of Odd Wheels”, arXiv:2511.18747 (2025).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.