Topic
Linkless embedding
About: Linkless embedding is a research topic. Over the lifetime, 143 publications have been published within this topic receiving 4462 citations.
Papers published on a yearly basis
Papers
TL;DR: It is shown that any setF, which can support a Fáry embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.
Abstract: Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fary embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide anO(n) space,O(n logn) time algorithm to effect this embedding. The grid size is asymptotically optimal and it had been previously unknown whether one can always find a polynomial sized grid to support such an embedding. On the other hand we show that any setF, which can support a Fary embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.
821 citations
TL;DR: An algorithm is presented that computes a region preserving grid embedding with the minimum number of bends in edges with use of network flow techniques, and runs in time $O(n^2 \log n)$, where n is the number of vertices of the graph.
Abstract: Given a planar graph G together with a planar representation P, a region preserving grid embedding of G is a planar embedding of G in the rectilinear grid that has planar representation isomorphic to P. In this paper, an algorithm is presented that computes a region preserving grid embedding with the minimum number of bends in edges. This algorithm makes use of network flow techniques, and runs in time $O(n^2 \log n)$, where n is the number of vertices of the graph. Constrained versions of the problem are also considered, and most results are extended to k-gonal graphs, i.e., graphs whose edges are sequences of segments with slope multiple of ${{180} / k}$ degrees. Applications of the above results can be found in several areas: VLSI circuit layout, architectural design, communication by light or microwave, transportation problems, and automatic layout of graphlike diagrams.
663 citations
TL;DR: It is shown that any two such embeddings of the same graph G are essentially the same, and a polynomial-time algorithm is given which will find such an embedding if it exists.
283 citations
TL;DR: A simple linear algorithm for embedding (or drawing) a planar graph in the plane based on the “vertex-addition” algorithm of Lempel, Even, and Cederbaum that can find all the embeddings of aPlanar graph.
259 citations
TL;DR: It is proved that Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges.
233 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 2 |
| 2019 | 2 |
| 2018 | 2 |
| 2017 | 2 |
| 2016 | 3 |