Global ETD Search
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Showing 1 to 6 of 6 for “"crossing number"”.
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Crossing Number Bounds of Mosaic Knot Diagrams
… Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more grid-like structure and no crossings. This grid structure …
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On the Breadth of the Jones Polynomial for Certain Classes of Knots and Links
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general. Only for very special classes of knots and links can we solve this problem. Often we can only hope to find a lower bound on the crossing number Cr(K) of a knot or a link K by computing the Jones …
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Some Results on Crossing Numbers
… edges is conjectured to produce the minimum number of edge crossings for a complete graph, which is its crossing number. This dissertation proves that no edge in this drawing can be redrawn to reduce the total number of edge crossings.
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Easy instances for model checking
… valence, planar graphs and graphs with bounded crossing number are all locally tree-like. And thus our results apply to these classes. <br> <br>For each of these two questions we consider the following questions: (i) decide, if a query hold in a structure (ii) compute an assignment that make a …
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Crossings in Clustered Level Graphs
… clusters and levels and their influence on edge crossings and cluster/edge crossings.
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Geometrically nonlinear configurations in rod-like structures
… scale) with increasing values for the crossing number (our measure of topology) and characterize their mechanical response through tension-displacement tests. The tensile force required to tighten the knot is governed by an intricate balance between topology, bending, and friction. A …