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» Contractions of Planar Graphs in Polynomial Time
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TAMC
2009
Springer
15 years 8 months ago
Linear Kernel for Planar Connected Dominating Set
We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set pr...
Daniel Lokshtanov, Matthias Mnich, Saket Saurabh
ISAAC
2004
Springer
141views Algorithms» more  ISAAC 2004»
15 years 7 months ago
Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation
We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they a...
Jérôme Monnot, Vangelis Th. Paschos, ...
111
Voted
CORR
2007
Springer
130views Education» more  CORR 2007»
15 years 1 months ago
On Computing the Distinguishing Numbers of Planar Graphs and Beyond: a Counting Approach
A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest...
Vikraman Arvind, Christine T. Cheng, Nikhil R. Dev...
SODA
2004
ACM
152views Algorithms» more  SODA 2004»
15 years 3 months ago
Approximation schemes for minimum 2-edge-connected and biconnected subgraphs in planar graphs
Given an undirected graph, finding either a minimum 2-edge-connected spanning subgraph or a minimum 2vertex-connected (biconnected) spanning subgraph is MaxSNP-hard. We show that ...
Artur Czumaj, Michelangelo Grigni, Papa Sissokho, ...
ISAAC
2009
Springer
113views Algorithms» more  ISAAC 2009»
15 years 6 months ago
On Shortest Disjoint Paths in Planar Graphs
For a graph G and a collection of vertex pairs {(s1, t1), . . . , (sk, tk)}, the k disjoint paths problem is to find k vertex-disjoint paths P1, . . . , Pk, where Pi is a path fr...
Yusuke Kobayashi, Christian Sommer 0002