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ISAAC
2007
Springer
158views Algorithms» more  ISAAC 2007»
14 years 1 months ago
On the Expressive Power of Planar Perfect Matching and Permanents of Bounded Treewidth Matrices
Valiant introduced some 25 years ago an algebraic model of computation along with the complexity classes VP and VNP, which can be viewed as analogues of the classical classes P and...
Uffe Flarup, Pascal Koiran, Laurent Lyaudet
JCT
2007
140views more  JCT 2007»
13 years 7 months ago
Homomorphisms and edge-colourings of planar graphs
We conjecture that every planar graph of odd-girth 2k + 1 admits a homomorphism to Cayley graph C(Z2k+1 2 , S2k+1), with S2k+1 being the set of (2k + 1)vectors with exactly two co...
Reza Naserasr
JCT
2006
81views more  JCT 2006»
13 years 7 months ago
Independent sets in triangle-free cubic planar graphs
: We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured b...
Christopher Carl Heckman, Robin Thomas
STOC
2009
ACM
171views Algorithms» more  STOC 2009»
14 years 8 months ago
On the geometry of graphs with a forbidden minor
We study the topological simplification of graphs via random embeddings, leading ultimately to a reduction of the Gupta-Newman-Rabinovich-Sinclair (GNRS) L1 embedding conjecture t...
James R. Lee, Anastasios Sidiropoulos
CCCG
2009
13 years 8 months ago
Planar Packing of Diameter-Four Trees
We prove that, for every two n-node non-star trees of diameter at most four, there exists an n-node planar graph containing them as edge-disjoint subgraphs.
Fabrizio Frati