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GD
2008
Springer
13 years 11 months ago
Crossing and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from di...
Sergio Cabello, Bojan Mohar
DM
2010
129views more  DM 2010»
13 years 10 months ago
Interpolating between bounds on the independence number
For a non-negative integer T, we prove that the independence number of a graph G = (V, E) in which every vertex belongs to at most T triangles is at least uV f(d(u), T) where d(u)...
Anett Boßecker, Dieter Rautenbach
ENDM
2008
114views more  ENDM 2008»
13 years 10 months ago
Strong oriented chromatic number of planar graphs without cycles of specific lengths
A strong oriented k-coloring of an oriented graph G is a homomorphism from G to H having k vertices labelled by the k elements of an abelian additive group M, such that for any p...
Mickaël Montassier, Pascal Ochem, Alexandre P...
DAM
2007
94views more  DAM 2007»
13 years 10 months ago
New formulations for the Kissing Number Problem
Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem ...
Sergei Kucherenko, Pietro Belotti, Leo Liberti, Ne...
DM
2007
116views more  DM 2007»
13 years 10 months ago
The Ramsey numbers for a cycle of length six or seven versus a clique of order seven
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. ...