Extending drawings of complete graphs into arrangements of pseudocircles

A.M. Arroyo Guevara, B. Richter, M. Sunohara, (n.d.).

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Abstract
We prove three principal results. First we exhibit a drawing of $K_{10}$ in the plane for which there do not exist extensions of the edges to simple closed curves with any two curves intersecting at most twice. Second, we exhibit a drawing of $K_9$ that has an extension of its edges to simple closed curves such that any two curves intersect in at most two points, but no extension to simple closed curves has every two curves intersecting in exactly two points. Third, we show that every h-convex drawing (introduced by Arroyo et al, submitted) has extensions of its edges to simple closed curves such that any two curves intersect in exactly two points. Using this result, we show that} a set of three axioms of simple closed curve extensions characterizes h-convexity.
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Date Published
2019-04-16
Page
35
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Cite this

Arroyo Guevara AM, Richter B, Sunohara M. Extending drawings of complete graphs into arrangements of pseudocircles.
Arroyo Guevara, A. M., Richter, B., & Sunohara, M. (n.d.). Extending drawings of complete graphs into arrangements of pseudocircles.
Arroyo Guevara, Alan M, Bruce Richter, and Matthew Sunohara. “Extending Drawings of Complete Graphs into Arrangements of Pseudocircles,” n.d.
A. M. Arroyo Guevara, B. Richter, and M. Sunohara, “Extending drawings of complete graphs into arrangements of pseudocircles.” .
Arroyo Guevara AM, Richter B, Sunohara M. Extending drawings of complete graphs into arrangements of pseudocircles.
Arroyo Guevara, Alan M., et al. Extending Drawings of Complete Graphs into Arrangements of Pseudocircles.
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2019-04-16T11:15:12Z


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