2015/10/06 by Ferdinand Ihringer, Ihringer, Ferdinand, Klaus Metsch +1
Mathematics · #05B25 #51E20 #52C10 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1510.01697
openalex publication_date 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate \0, 1, …, t \-cliques of generators on dual polar graphs of finite classical polar spaces of rank d. These cliques are also known as Erdős-Ko-Rado sets in polar spaces of generators with pairwise intersections in at most codimension t. Our main result is that we classify all such cliques of maximum size for t ≤ √(8d/5)-2 if q ≥ 3, and t ≤ √(8d/9)-2 if q = 2. We have the following byproducts. (a) For q ≥ 3 we provide estimates of Hoffman's bound on these \0, 1, …, t \-cliques for all t. (b) For q ≥ 3 we determine the largest, second largest, and smallest eigenvalue of the graphs which have the generators of a polar space as vertices and where two generators are adjacent if and only if they meet in codimension at least t+1. Furthermore, we provide nice explicit formulas for all eigenvalues of these graphs. (c) We provide upper bounds on the size of the second largest maximal \0, 1, …, t \-cliques for some t.