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» Diameter bounds for planar graphs
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COCOON
2007
Springer
15 years 6 months 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...
COMGEO
2007
ACM
14 years 11 months ago
Drawings of planar graphs with few slopes and segments
We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-...
Vida Dujmovic, David Eppstein, Matthew Suderman, D...
CORR
2008
Springer
131views Education» more  CORR 2008»
14 years 12 months ago
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolati...
Samir Datta, Raghav Kulkarni, Sambuddha Roy
FOCS
2008
IEEE
15 years 6 months ago
Nearly Tight Low Stretch Spanning Trees
We prove that any graph G with n points has a distribution T over spanning trees such that for any edge (u, v) the expected stretch ET ∼T [dT (u, v)/dG(u, v)] is bounded by ˜O(...
Ittai Abraham, Yair Bartal, Ofer Neiman
JGT
2008
107views more  JGT 2008»
14 years 11 months ago
On planar intersection graphs with forbidden subgraphs
Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has ...
János Pach, Micha Sharir