Titlebook: ;

patriot

verdict

Point-Set Embedding of Trees with Edge Constraintson . that includes the given partial drawing of .′. We concentrate on trees and show how to compute the output in .(.. log.) time and with at most 1 + 2 ⌈./2 ⌉ bends per edge, where . is the number of vertices of the given subdrawing. We also prove that there are instances of the problem which require at least . − 3 bends for some of the edges.

哑剧

Representation of Planar Hypergraphs by Contacts of Triangles of those hypergraphs which are representable by contact of segments in the plane, We propose some possible generalization directions and open problems, related to the order dimension of the incidence posets of hypergraphs.

尖酸一点

https://doi.org/10.1007/978-81-322-2598-0lgorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).

繁重

nutrients

Crossing Number of Graphs with Rotation Systemsf multigraphs with rotation systems on a fixed number . of vertices. For . = 1 and . = 2 the crossing number can be computed in polynomial time and approximated to within a factor of 2 in linear time. For larger . we show how to approximate the crossing number to within a factor of . in time .(..) on a graph with . edges.

含糊其辞

Characterization of Unlabeled Level Planar Graphse labelings. Our contributions are twofold. First, we provide linear time drawing algorithms for . graphs. Second, we provide a complete characterization of . graphs by showing that any other graph must contain a subgraph homeomorphic to one of seven forbidden graphs.

reflection

Moving Vertices to Make Drawings Planeow that . is NP-hard and hard to approximate. Second, we establish a connection to the graph-drawing problem ., which yields similar results for that problem. Third, we give bounds for the behavior of . on trees and general planar graphs.

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