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DTSTAMP:20210120T013625Z
UID:5c8a5b8a7a966710138004@ist.ac.at
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DESCRIPTION:Speaker: Amir Jafari\nhosted by Uli Wagner\nAbstract: This will
be a report of a recent joint work with Soheil Azarpendar. For integers n
\, k\, r where n>kr-1 The Kneser hypergraph KG^r(n\,k) was defined by Lova
sz\, Alon and Frankl as the r-uniform hypergraph with all k-subsets of {1\
,...\,n} as vertices and its hyperedges are all r-subsets {A_1\,...\,A_r}
of vertices that are pairwise disjoint. It was proved by them using topolo
gical methods that its chromatic number is the ceiling of (n-r(k-1))/(r-1)
.Ziegler conjectured that if we take the induced sub hypergraph whose vert
ices are all r-stable (i.e subsets that for any two distinct elements i an
d j in them r-1< |i-j|2. In this talk we prove a weaker version of this co
njecture\, due to Frick et al\, that states if {P_1\,...\,P_t} is a partit
ion of {1\,..\,n} where the size of each P_i is at most r and we take the
induced sub hypergraph of KG^r(n\,k) whose vertices are those k-subsets th
at have at most one element from each P_i then we still get the same chrom
atic number. Our proof for this conjecture is combinatorial and uses Z_p T
ucker lemma. If time permits some topological methods related to similar p
roblems will be explained.
LOCATION:Mondi Seminar Room 3\, Central Building\, IST Austria
ORGANIZER:hwagner@ist.ac.at
SUMMARY:GeomTop Seminar: "\;Chromatic number of Kneser hypergraphs and
a conjecture of Frick"\;
URL:https://talks-calendar.app.ist.ac.at/events/2711
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