Connectivity augmentation in planar straight line graphs
نویسندگان
چکیده
منابع مشابه
Connectivity augmentation in planar straight line graphs∗
It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph with at most bn/2c new edges...
متن کاملTri-Edge-Connectivity Augmentation for Planar Straight Line Graphs
It is shown that if a planar straight line graph (PSLG) with n vertices in general position in the plane can be augmented to a 3-edge-connected PSLG, then 2n−2 new edges are enough for the augmentation. This bound is tight: there are PSLGs with n ≥ 4 vertices such that any augmentation to a 3-edge-connected PSLG requires 2n− 2 new edges.
متن کاملMinimum Weight Connectivity Augmentation for Planar Straight-Line Graphs
Connectivity augmentation is a classical problem in combinatorial optimization (see [4, 5]). Given a graph G = (V,E) and a parameter τ ∈ N, add a set of new edges E+ such that the augmented graph G′ = (V,E ∪ E+) is τ -connected (resp., τ -edge-connected). Over planar straightline graphs (PSLGs), it is NP-complete to find the minimum number of edges for τ -connectivity or τ -edge-connectivity au...
متن کاملConnectivity augmentation in plane straight line graphs
It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph by adding at most bn/2c edge...
متن کاملAugmenting Planar Straight Line Graphs to 2-Edge-Connectivity
We show that every planar straight line graph (PSLG) with n vertices can be augmented to a 2-edge-connected PSLG with the addition of at most b(4n− 4)/3c new edges. This bound is the best possible. Edge-connectivity augmentation is a classic problem in combinatorial optimization motivated by applications in fault-tolerant network design. Given an undirected graph G = (V,E) and a number τ ∈ N, w...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.09.002