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Seminar by Kaushik Majumder

Thursday, April 5, 2018 - 16:35 to 17:35
Seminar Room, School of Mathematical Sciences
Kaushik Majumder
ISI Kolkata
Problems and Results in uniform intersecting families.

Kneser Graph $KG_{n,k}$ is a graph whose vertex set is all possible $k-$subsets from an $n-$set (here $n-$set means a set of size $n$) say $[n]:=\{1,\ldots,n\}$ and $X, Y$ are $k-$subsets of $[n]$ form an edge if and only if $X$ is disjoint from $Y$. Therefore a co-clique (independent set) of such graph form an intersecting family of $k-$sets. The chromatic number of this graph is $n-2k+2$. In order to decompose $KG_{n,k}$ into its colour classes, we first deal with the following question in Extremal Combinatorics regarding the size of the colour classes. Question. What is the possible maximum size of an intersecting family of $k-$sets from an $n-$set? The complete answer of the above question lies within the famous Erd\H{o}s-Ko-Rado Theorem. The specific answer raises other problems naturally. In this talk, we shall discuss about the related problems and results on intersecting families from classical days to these contemporary days. We also plan to disclose the techniques which leads to produce these results.

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