
βStars or On Extending a Drawing of a Connected Subgraph
We consider the problem of extending the drawing of a subgraph of a give...
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On the number of edges of separated multigraphs
We prove that the number of edges of a multigraph G with n vertices is a...
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The number of crossings in multigraphs with no empty lens
Let G be a multigraph with n vertices and e>4n edges, drawn in the plane...
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StarStruck by Fixed Embeddings: Modern Crossing Number Heuristics
We present a thorough experimental evaluation of several crossing minimi...
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Strong HananiTutte for the Torus
If a graph can be drawn on the torus so that every two independent edges...
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Crossing Minimization in Perturbed Drawings
Due to data compression or low resolution, nearby vertices and edges of ...
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Acyclic, Star and Injective Colouring: A Complexity Picture for HFree Graphs
A kcolouring c of a graph G is a mapping V(G) to 1,2,... k such that c(...
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On the Maximum Number of Crossings in StarSimple Drawings of K_n with No Empty Lens
A starsimple drawing of a graph is a drawing in which adjacent edges do not cross. In contrast, there is no restriction on the number of crossings between two independent edges. When allowing empty lenses (a face in the arrangement induced by two edges that is bounded by a 2cycle), two independent edges may cross arbitrarily many times in a starsimple drawing. We consider starsimple drawings of K_n with no empty lens. In this setting we prove an upper bound of 3((n4)!) on the maximum number of crossings between any pair of edges. It follows that the total number of crossings is finite and upper bounded by n!.
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