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» On Planar Quasi-Parity Graphs
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JCT
2007
140views more  JCT 2007»
15 years 1 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»
15 years 1 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»
16 years 2 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
15 years 3 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
ATMOS
2010
134views Optimization» more  ATMOS 2010»
15 years 28 days ago
Vertex Disjoint Paths for Dispatching in Railways
We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization...
Holger Flier, Matús Mihalák, Anita S...