Efficient Planarity Testing
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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.read more
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Graph theory with applications
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Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
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Complexity of finding embeddings in a k -tree
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References
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Journal ArticleDOI
Depth-First Search and Linear Graph Algorithms
TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.
Book
Theory of graphs
TL;DR: In this article, the axiom of choice of choice is used to define connectedness path problems in directed graphs and cyclic graphs, as well as Galois correspondences of connectedness paths.
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How to Draw a Graph
TL;DR: In this paper, the authors define nodally 3-connected graphs as simple and non-separable graphs, and show how to obtain a convex representation of such graphs without Kuratowski subgraphs.
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Algorithm 447: efficient algorithms for graph manipulation
TL;DR: Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths and each iteration produces a new path between two vertices already on paths.