Diameter-boundedness conjecture for tight distance-regular graphs
Diameter-boundedness conjecture for tight distance-regular graphs
Let be a tight distance-regular graph. Let , where is an intersection number of and is the second largest eigenvalue of . Assume that .
Diameter-boundedness conjecture. The diameter of is bounded by a function in .
The conjecture seeks a uniform diameter bound for tight distance-regular graphs in terms of the parameter . 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.
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