Compatible Connectivity Augmentation of Planar Disconnected Graphs
نویسندگان
چکیده
منابع مشابه
Compatible Connectivity-Augmentation of Planar Disconnected Graphs
Motivated by applications to graph morphing, we consider the following compatible connectivity-augmentation problem: We are given a labelled n-vertex planar graph, G, that has r ≥ 2 connected components, and k ≥ 2 isomorphic planar straight-line drawings, G1, . . . ,Gk , of G. We wish to augment G by adding vertices and edges to make it connected in such a way that these vertices and edges can ...
متن کاملConnectivity 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 کاملSubgraph Induced Planar Connectivity Augmentation
Given a planar graph G = (V,E) and a vertex set W ⊆ V , the subgraph induced planar connectivity augmentation problem asks for a minimum cardinality set F of additional edges with end vertices in W such that G′ = (V,E∪F ) is planar and the subgraph of G′ induced by W is connected. The problem arises in automatic graph drawing in the context of c-planarity testing of clustered graphs. We describ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2015
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-015-9716-8