AbstractA classical result of Hajnal and Thomassen asserts that for every$k$ there exists $K$ such that the vertices of every $K$-connected graph can be partitioned into two sets inducing $k$-connected subgraphs. Moreover they showed $K=O(k)$. There is now a whole area of combinatorial problems concerned with questions of this type; namely, to understand whether for a certain (di)graph property...
AbstractThe Brunn-Minkowski inequality states that for (open) sets A and B in Rd, we have4 + B|1/d > |A|l/d + |B|l/d. Equality holds if and only if A and B are convex and homotheticsets in R". In this talk, we present a sharp stability result for the Brunn-Minkowski inequality.concluding a long line of research on this problem, We show that if we are close to eauality in theBrunn-Minkowski ineg...
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