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mgr inż. Andrzej Jastrzębski
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Catalog Publications
Year 2018
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Turán numbers for odd wheels
PublicationThe Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. A wheel W_n is a graph on n vertices obtained from a C_{n−1} by adding one vertex w and making w adjacent to all vertices of the C_{n−1}. We obtain two exact values for small wheels: ex(n,W_5)=\lfloor n^2/4+n/2\rfloor, ex(n,W_7)=\lfloor n^2/4+n/2+1 \rfloor. Given that ex(n,W_6) is already known, this...
Year 2016
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Edge-coloring of 3-uniform hypergraphs
PublicationWe consider edge-colorings of 3-uniform hypergraphs which is a natural generalization of the problem of edge-colorings of graphs. Various classes of hypergraphs are discussed and we make some initial steps to establish the border between polynomial and NP-complete cases. Unfortunately, the problem appears to be computationally difficult even for relatively simple classes of hypergraphs.
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Equitable coloring of graphs. Recent theoretical results and new practical algorithms
PublicationIn this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
Year 2015
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Towards the boundary between easy and hard control problems in multicast Clos networks
PublicationIn this article we study 3-stage Clos networks with multicast calls in general and 2-cast calls, in particular. We investigate various sizes of input and output switches and discuss some routing problems involved in blocking states. To express our results in a formal way we introduce a model of hypergraph edge-coloring. A new class of bipartite hypergraphs corresponding to Clos networks is studied. We identify some polynomially...
Year 2010
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Rearrangeability in multicast Clos networks is NP-complete
PublicationPrzestrajalność w polach Closa z połączeniami jeden do jeden jest problemem wielomianowym. W pracy pokazano, że w polach z połączeniami jeden do wiele problem ten jest NP zupełny.Three-stage elos networks are commutation networks with circuit switching. So far, graph theory has been very useful tool for solving issues related to these networks with unicast connections. This is so because if elos network is represented as a bipartite...
Year 2008
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Duże rozgłoszeniowe pola Closa
PublicationW pracy pokazano nowe podejście do blokowalności dużych rozgłoszeniowych pól Closa. Przedstawione zostały także dowody na blokowalność pola C(n,r_1,n^2-1,n,r_2) oraz pola C(n,r_1,n^2,n,r_2), w których użyto ekstremalną teorię grafów i hipergrafów.
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Rearrangeable clos networks C(n,r_1,n^2-1,n,r_2) with certain restrictions for connections
PublicationW pracy została zaproponowana nowa metoda sprawdzania przestrajalności pól Closa dla połączeń jeden do wiele. W rozważaniach zakładamy grupowanie połączeń.In the article we will propose new method of checking rearrangeability of multicast Clos networks. In the literature there is no precise method for checking rearrangeability. We focused on three-stage Clos networks without any constraints about fan-out capability. We show the...
Year 2007
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Graph models of clos networks
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