43 research outputs found
Hitting minors, subdivisions, and immersions in tournaments
The Erd\H{o}s-P\'osa property relates parameters of covering and packing of
combinatorial structures and has been mostly studied in the setting of
undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim,
and Seymour to show that, for every directed graph (resp.
strongly-connected directed graph ), the class of directed graphs that
contain as a strong minor (resp. butterfly minor, topological minor) has
the vertex-Erd\H{o}s-P\'osa property in the class of tournaments. We also prove
that if is a strongly-connected directed graph, the class of directed
graphs containing as an immersion has the edge-Erd\H{o}s-P\'osa property in
the class of tournaments.Comment: Accepted to Discrete Mathematics & Theoretical Computer Science.
Difference with the previous version: use of the DMTCS article class. For a
version with hyperlinks see the previous versio
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The embedding of complete bipartite graphs onto grids with a minimum grid cutwidth
Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained
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Investigation of 4-cutwidth critical graphs
A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs
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Minimal congestion trees
Analyzes the results of M.I. Ostrovskii\u27s theorem of inequalities which estimate the minimal edge congestion for finite simple graphs. Uses the generic results of the theorem to examine and further reduce the parameters of inequalities for specific families of graphs, particularly complete graphs and complete bipartite graphs. Also, explores a possible minimal congestion tree for some grids while forming a conjecture for all grids
Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes
Interconnection networks provide an effective mechanism for exchanging data
between processors in a parallel computing system. One of the most efficient
interconnection networks is the hypercube due to its structural regularity,
potential for parallel computation of various algorithms, and the high degree
of fault tolerance. Thus it becomes the first choice of topological structure
of parallel processing and computing systems. In this paper, lower bounds for
the dilation, wirelength, and edge congestion of an embedding of a graph into a
hypercube are proved. Two of these bounds are expressed in terms of the
bisection width. Applying these results, the dilation and wirelength of
embedding of certain complete multipartite graphs, folded hypercubes, wheels,
and specific Cartesian products are computed
Methods and problems of wavelength-routing in all-optical networks
We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions