منابع مشابه
Grid Minors in Damaged Grids
We prove upper and lower bounds on the size of the largest square grid graph that is a subgraph, minor, or shallow minor of a graph in the form of a larger square grid from which a specified number of vertices have been deleted. Our bounds are tight to within constant factors. We also provide less-tight bounds on analogous problems for higher-dimensional grids.
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Intuitively, a tangle of large order in a graph is a highly-connected part of the graph, and it is known that if a graph has a tangle of large order then it has a large grid minor. Here we show that for any k, if G has a tangle of large order and Z is a set of vertices of cardinality k that cannot be separated from the tangle by any separation of order less than k, then G has a large grid minor...
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This document describes issues related to running a heterogeneous, but production-level Grid. It is based on experience gained running and maintaining heterogeneous GridLab testbed as well as large ad hoc demonstration testbeds. The Grids discussed in this document are built not using dedicated machines or clusters, but their building blocks are other Grids or their parts. Last amendment date: ...
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In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the running times of a broad class of fixed-parameter algorithms. Our novel technique of using appro...
متن کاملGrid-distortion on nonrectangular grids
Grid-distortion is an image warping technique which is driven by the mapping between equivalent families of curves, arranged in a grid structure. Until recently only curves sets arranged in a regular rectangular grid were considered. In the present work we construct a smooth (C 1) grid-distortion mappings deened by curves arranged in a non-regular structure , and fully characterize the most gen...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/3872