Topic
Planarity testing
About: Planarity testing is a research topic. Over the lifetime, 1626 publications have been published within this topic receiving 30116 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: The consecutive ones test for the consecutive ones property in matrices and for graph planarity is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.
1,622 citations
Book•
[...]
01 Jun 1979
TL;DR: A thoroughly revised second edition of Shimon Even's Graph Algorithms, with a foreword by Richard M. Karp and notes by Andrew V Goldberg, explains algorithms in a formal but simple language with a direct and intuitive presentation.
Abstract: Shimon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, including graphs and shortest paths, trees, depth-first-search, and breadth-first search. The main part of the book is devoted to network flows and applications of network flows, and it ends with chapters on planar graphs and testing graph planarity.
1,428 citations
TL;DR: An efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane is described, which used depth-first search and has time and space bounds.
Abstract: This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm used depth-first search and has O(V) time and space bounds, where V is the number of vertices in G. An ALGOL implementation of the algorithm succesfully tested graphs with as many as 900 vertices in less than 12 seconds.
1,183 citations
Book•
01 Jan 1972
TL;DR: In this paper, Paths and cycles, trees, planarity, and coloring graphs are defined and examples of path-and-cycle exercises are given, together with solutions to selected exercises.
Abstract: Introduction * Definitions and examples* Paths and cycles* Trees* Planarity* Colouring graphs* Matching, marriage and Menger's theorem* Matroids Appendix 1: Algorithms Appendix 2: Table of numbers List of symbols Bibliography Solutions to selected exercises Index
1,024 citations
TL;DR: A dynamic programming algorithm is presented which computes the size of the maximum for the given A-B base sequence and which also allows reconstructing a particular folded form of the original string which realizes the maximum matching size.
Abstract: A simplified (two-base) version of the problem of planar folding of long chains (e.g., RNA and DNA biomolecules) is formulated as a matching problem. The chain is prescribed as a loop or circular sequence of letters A and B, n units long. A matching here means a set of A-B base pairings or matches obeying a planarity condition: no two matches may cross each other if drawn on the interior of the loop. Also, no two adjacent letters may be matched. We present a dynamic programming algorithm requiring $O( {n^3 } )$ steps and $O( {n^2 } )$ storage which computes the size of the maximum for the given A-B base sequence and which also allows reconstructing a particular folded form of the original string which realizes the maximum matching size. The algorithm can be adapted to deal with sequences with larger alphabets and with weighted matchings.An algorithm is also presented for a modified problem closer to the biochemical problem of interest: We demand that every match must be adjacent to another match, forcing ...
620 citations