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» On Planar Quasi-Parity Graphs
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JCT
2007
140views more  JCT 2007»
15 years 6 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 6 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
167
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STOC
2009
ACM
171views Algorithms» more  STOC 2009»
16 years 6 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 7 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 5 months 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...