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» On Planar Quasi-Parity Graphs
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COCOON
2007
Springer
16 years 25 days ago
On the Number of Cycles in Planar Graphs
We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a...
Kevin Buchin, Christian Knauer, Klaus Kriegel, And...
JGT
2010
103views more  JGT 2010»
15 years 5 months ago
Characterizing 3-connected planar graphs and graphic matroids
: A well-known result of Tutte states that a 3-connected graph G is planar if and only if every edge of G is contained in exactly two induced non-separating circuits. Bixby and Cun...
Manoel Lemos, Talmage James Reid, Haidong Wu
ALGORITHMICA
1998
94views more  ALGORITHMICA 1998»
15 years 6 months ago
A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs
In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorit...
Philip N. Klein, Sairam Subramanian
ISAAC
2009
Springer
103views Algorithms» more  ISAAC 2009»
16 years 1 months ago
Tri-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 enou...
Marwan Al-Jubeh, Mashhood Ishaque, Kristóf ...
STOC
2006
ACM
186views Algorithms» more  STOC 2006»
16 years 7 months ago
A subset spanner for Planar graphs, : with application to subset TSP
Let > 0 be a constant. For any edge-weighted planar graph G and a subset S of nodes of G, there is a subgraph H of G of weight a constant times that of the minimum Steiner tree...
Philip N. Klein