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» On the Number of Cycles in Planar Graphs
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CORR
2010
Springer
103views Education» more  CORR 2010»
13 years 7 months ago
On Graph Crossing Number and Edge Planarization
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
JCT
2007
118views more  JCT 2007»
13 years 7 months ago
Excluding a planar graph from GF(q)-representable matroids
Abstract. We prove that a binary matroid with huge branchwidth contains the cycle matroid of a large grid as a minor. This implies that an infinite antichain of binary matroids ca...
Jim Geelen, Bert Gerards, Geoff Whittle
DAM
2007
107views more  DAM 2007»
13 years 7 months ago
Eliminating graphs by means of parallel knock-out schemes
In 1997 Lampert and Slater introduced parallel knock-out schemes, an iterative process on graphs that goes through several rounds. In each round of this process, every vertex elim...
Hajo Broersma, Fedor V. Fomin, Rastislav Kralovic,...
SIAMDM
2010
89views more  SIAMDM 2010»
13 years 2 months ago
Routing Numbers of Cycles, Complete Bipartite Graphs, and Hypercubes
The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In t...
Wei-Tian Li, Linyuan Lu, Yiting Yang