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» Crossing numbers of random graphs
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DCG
2006
110views more  DCG 2006»
13 years 8 months ago
High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in Rn . It has recently been shown that properties of the centrosymmetric polytope P = AC are ...
David L. Donoho
JCT
2007
111views more  JCT 2007»
13 years 7 months ago
Removing even crossings
An edge in a drawing of a graph is called even if it intersects every other edge of the graph an even number of times. Pach and T´oth proved that a graph can always be redrawn so...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
CPC
2010
117views more  CPC 2010»
13 years 5 months ago
On the Number of Perfect Matchings in Random Lifts
Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint)...
Catherine S. Greenhill, Svante Janson, Andrzej Ruc...
DM
2008
103views more  DM 2008»
13 years 8 months ago
Improper colouring of (random) unit disk graphs
For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
Ross J. Kang, Tobias Müller, Jean-Séba...
APVIS
2004
13 years 9 months ago
Optimal Leaf Ordering for Two and a Half Dimensional Phylogenetic Tree Visualisation
Two and a half dimensional graph visualisation is the stacking of a set of related graphs into the third dimension to support visual comparison. A new aesthetic criterion is intro...
Tim Dwyer, Falk Schreiber