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Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
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Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut
 PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION
, 1993
"... In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3 ..."
Abstract

Cited by 8 (1 self)
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In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3;3 , turn out to define facets of this polytope. We also present computational experience with a branch and cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K 5 or K 3;3 . These structures give us inequalities which are used as cutting planes.
The Polyhedral Approach to the Maximum Planar Subgraph Problem: New Chances for Related Problems
 In DIMACS Graph Drawing '94, volume 894 of LNCS
, 1994
"... . In [JM94] we used a branch and cut algorithm in order to determine a maximum weight planar subgraph of a given graph. One of the motivations was to produce a nice drawing of a given graph by drawing the found maximum planar subgraph, and then augmenting this drawing by the removed edges. Our exper ..."
Abstract

Cited by 3 (2 self)
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. In [JM94] we used a branch and cut algorithm in order to determine a maximum weight planar subgraph of a given graph. One of the motivations was to produce a nice drawing of a given graph by drawing the found maximum planar subgraph, and then augmenting this drawing by the removed edges. Our experiments indicate that drawing algorithms for planar graphs which require 2 or 3connectivity, resp. degreeconstraints, in addition to planarity often give "nicer" results. Thus we are led to the following problems: (1) Find a maximum planar subgraph with maximum degree d 2 IN. (2) Augment a planar graph to a kconnected planar graph. (3) Find a maximum planar kconnected subgraph of a given k connected graph. (4) Given a graph G, which is not necessarily planar and not necessarily kconnected, determine a new graph H by removing r edges and adding a edges such that the new graph H is planar, spanning, kconnected, each node v has degree at most D(v) and r + a is minimum. Problems (1), (2...