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Fleiner T.,Budapest University of Technology and Economics | Fleiner T.,MTA ELTE Egervary Research Group | Janko Z.,Eotvos Lorand University
Order | Year: 2016

A recent result of Aharoni Berger and Gorelik (Order 31(1), 35–43, 2014) is a weighted generalization of the well-known theorem of Sands Sauer and Woodrow (Theory Ser. B 33(3), 271–275, 1982) on monochromatic paths. The authors prove the existence of a so called weighted kernel for any pair of weighted posets on the same ground set. In this work, we point out that this result is closely related to the stable marriage theorem of Gale and Shapley (Amer. Math. Monthly 69(1), 9–15, 1962), and we generalize Blair’s theorem by showing that weighted kernels form a lattice under a certain natural order. To illustrate the applicability of our approach, we prove further weighted generalizations of the Sands Sauer Woodrow result. © 2015, Springer Science+Business Media Dordrecht.

Kiraly Z.,Eotvos Lorand University | Kiraly Z.,MTA ELTE Egervary Research Group | Kovacs E.R.,Eotvos Lorand University
Information Processing Letters | Year: 2015

Network coding is a method for information transmission in a network, based on the idea of enabling internal nodes to forward a function of the incoming messages, typically a linear combination. In this paper we discuss generalizations of the network coding problem with additional constraints on the coding functions called network code completion problem, NCCP. We give both randomized and deterministic algorithms for maximum throughput-achieving network code construction for the NCCP in the multicast case. We also introduce the related problem of fixable pairs, investigating when a certain subset of coding coefficients in the linear combination functions can be fixed to arbitrary non-zero values such that the network code can always be completed to achieve maximum throughput. We give a sufficient condition for a set of coding coefficients to be fixable. For both problems we present applications in different wireless and heterogeneous network models. © 2014 Elsevier B.V. All rights reserved.

Frank A.,Eotvos Lorand University | Frank A.,MTA ELTE Egervary Research Group | Kiraly C.,Eotvos Lorand University
Operations Research Letters | Year: 2013

A tree-composition is a tree-like family that serves to describe the obstacles to k-edge-connected orientability of mixed graphs. Here we derive a structural result on tree-compositions that gives rise to a simple algorithm for computing an obstacle when the orientation does not exist. As another application, we show a min-max theorem on the minimal in-degree of a given node set in a k-edge-connected orientation of an undirected graph. This min-max formula can be simplified in the special case of k=1. © 2013 Elsevier B.V. All rights reserved.

Berczi K.,MTA ELTE Egervary Research Group | Bernath A.,MTA ELTE Egervary Research Group | Vizer M.,MTA Alfred Renyi Institute of Mathematics
Electronic Journal of Combinatorics | Year: 2015

An undirected simple graph G = (V,E) is called antimagic if there exists an injective function f: E → {1,…|E|} such that (formula presented) for any pair of different nodes u, v ∈ V. In this note we prove - with a slight modification of an argument of Cranston et al. - that k-regular graphs are antimagic for k ≥ 2. © 2015, Australian National University. All rights reserved.

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