Diameter-boundedness conjecture for tight distance-regular graphs

From papers

Let Γ\Gamma be a tight distance-regular graph. Let b=b1/(1+θ1)b=b_1/(1+\theta_1), where b1b_1 is an intersection number of Γ\Gamma and θ1\theta_1 is the second largest eigenvalue of Γ\Gamma. Assume that b2b\geq 2.

Diameter-boundedness conjecture. The diameter of Γ\Gamma is bounded by a function in bb.

The conjecture seeks a uniform diameter bound for tight distance-regular graphs in terms of the parameter bb. The paper proves such a bound under additional hypotheses and presents this as a goal for further generalization; the unrestricted statement remains open in the supplied source.

Progress summary

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

Sources & referencesView supporting material

Primary source

Jack H. Koolen, Jae-Ho Lee, Shuang-Dong Li, Yun-Han Li, Xiaoye Liang and Ying-Ying Tan, “On the (non-)existence of tight distance-regular graphs: a local approach”, arXiv:2312.05595 (2024).

Additional references

3 papers in this index state this conjecture (2011–2023). The statement above is taken from the most recent of them; the others are arXiv:1602.07243, arXiv:1101.2357.

Solutions 0

No solutions have been posted yet.