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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\, ISTA
ORGANIZER:hwagner@ist.ac.at
SUMMARY:Amir Jafari: GeomTop Seminar: &quot\;Chromatic number of Kneser hyp
 ergraphs and a conjecture of Frick&quot\;
URL:https://talks-calendar.ista.ac.at/events/2711
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