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  • On intersection densities of transitive groups and vertex-transitive graphs [Elektronski vir]
    Kutnar, Klavdija, 1980-
    The Erdös-Ko-Rado-Ko-Rado theorem, one of the central results in extremal combinatorics, which gives a bound on the size of a family of intersecting ▫$k$▫-subsets of a set and classifies the families ... satisfying the bound, has been extended in various ways. In this talk I will discuss an extension of this theorem to the ambient of transitive permutation groups and vertex-transitive graphs. Let ▫$V$▫ be a finite set and ▫$G$▫ a group acting on ▫$V$▫. Two elements ▫$g,h\in G$▫ are said to be {\em intersecting} if ▫$g(v) = h(v)$▫ for some ▫$v \in V$▫. More generally, a subset ▫${\cal F}$▫ of ▫$G$▫ is an ▫{\em intersecting set}▫ provided every pair of elements of ▫${\cal F}$▫ is intersecting. The {\em intersection density} ▫$\rho(G)$▫ of a transitive permutation group ▫$G$▫ is the maximum value of the quotient ▫$|{\cal F}|/|G_v|$▫ where ▫${\cal F}$▫ runs over all intersecting sets in ▫$G$▫ and ▫$G_v$▫ is a stabilizer of ▫$v\in V$▫. The {\em intersection density array} ▫$[\rho_0,\rho_1, ...,\rho_{k-1}]$▫ of a vertex-transitive graph ▫$X$▫ is defined as a "collection'' of increasing intersection densities of transitive subgroups of ▫$Aut X$▫, that is, for any transitive subgroup ▫$G$▫ of ▫$Aut X$▫, we have ▫$\rho(G) = \rho_i$▫ for some ▫$i \in \mathbb Z_k$▫, with ▫$\rho_i<\rho_{i+1}$▫. In this talk I will present some recent results about intersection densities of certain transitive permutation groups and vertex-transitive graphs of small valencies.
    Source: SIGMAP 2022 [Elektronski vir] (1 spletni vir)
    Type of material - conference contribution
    Publish date - 2022
    Language - english
    COBISS.SI-ID - 115598083

    Link(s):

    https://sigmap.community.uaf.edu/plenary-speakers/

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