
Simple Compact Monotone Tree Drawings
A monotone drawing of a graph G is a straightline drawing of G such tha...
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Saturated kPlane Drawings with Few Edges
A drawing of a graph is kplane if no edge is crossed more than k times....
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The Partition Spanning Forest Problem
Given a set of colored points in the plane, we ask if there exists a cro...
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Searching by Heterogeneous Agents
In this work we introduce and study a pursuitevasion game in which the ...
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Ordered Level Planarity, Geodesic Planarity and BiMonotonicity
We introduce and study the problem Ordered Level Planarity which asks fo...
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(g,f)Chromatic spanning trees and forests
A heterochromatic (or rainbow) graph is an edgecolored graph whose edge...
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Anglemonotone Paths in Nonobtuse Triangulations
We reprove a result of Dehkordi, Frati, and Gudmundsson: every two verti...
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Plane Spanning Trees in EdgeColored Simple Drawings of K_n
Károlyi, Pach, and Tóth proved that every 2edgecolored straightline drawing of the complete graph contains a monochromatic plane spanning tree. It is open if this statement generalizes to other classes of drawings, specifically, to simple drawings of the complete graph. These are drawings where edges are represented by Jordan arcs, any two of which intersect at most once. We present two partial results towards such a generalization. First, we show that the statement holds for cylindrical simple drawings. (In a cylindrical drawing, all vertices are placed on two concentric circles and no edge crosses either circle.) Second, we introduce a relaxation of the problem in which the graph is kedgecolored, and the target structure must be hypochromatic, that is, avoid (at least) one color class. In this setting, we show that every ⌈ (n+5)/6⌉edgecolored monotone simple drawing of K_n contains a hypochromatic plane spanning tree. (In a monotone drawing, every edge is represented as an xmonotone curve.)
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