The polyhedral approach to the maximum planar subgraph problem: New chances for related problems
Find a maximum planar subgraph with maximum degree d ∈ IN.
Augment a planar graph to a K-connected planar graph.
Find a maximum planar k-connected subgraph of a given k-connected graph.
Given a graph G, which is not necessarily planar and not necessarily k-connected, determine a new graph H by removing r edges and adding a edges such that the new graph H is planar, spanning, k-connected, each node v has degree at most D(v) and r+a is minimum.
Problems (1), (2) and (3) have been discussed in the literature, we argue that a solution to the newly defined problem (4) is most useful for our goal. For all four problems we give a polyhedral formulation by defining different linear objective functions over the same polytope which is the intersection of the planar subgraph polytope [JM93], the k-connected subgraph polytope [S92] and the degree-constrained subgraph polytope. We point out why we are confident that a branch and cut algorithm for the new problem will be an implementable and useful tool in automatic graph drawing.
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