Titlebook: Building Bridges II; Mathematics of Lászl Imre Bárány,Gyula O. H. Katona,Attila Sali Book 2019 J�nos Bolyai Mathematical Society and Sprin

HARD

Sequential Importance Sampling for Estimating the Number of Perfect Matchings in Bipartite Graphs: practice but has eluded analysis. This paper offers examples where the analysis can be carried out and the first general bounds for the sample size required. This uses a novel importance sampling proof of Brégman’s inequality due to Lovász.

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Coloured and Directed Designs,ypergraphs with coloured or directed edges. For example, we give fairly general conditions for decomposing an edge-coloured graph into rainbow triangles, and for decomposing an .-digraph into tight .-cycles.

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Efficient Convex Optimization with Oracles,n is given by an evaluation oracle and the set by a membership oracle. The algorithm takes . oracle calls and . additional arithmetic operations. This results in more efficient reductions among the five basic oracles for convex sets and functions defined by Grötschel, Lovász and Schrijver (Algorithms Comb 2, (1988), [.]).

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Finding , Partially Disjoint Paths in a Directed Planar Graph, show that for fixed ., this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is solvable in polynomial time for directed graphs embedded on a fixed compact surface. Moreover, one may specify for each edge a subset of . prescribing which of the . paths are allowed to traverse this edge.

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