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COMBINATORICA
2008
88views more  COMBINATORICA 2008»
11 years 12 months ago
Geometric graphs with no two parallel edges
We give a simple proof for a theorem of Katchalski, Last, and Valtr, asserting that the maximum number of edges in a geometric graph G on n vertices with no pair of parallel edges...
Rom Pinchasi
IPL
2008
104views more  IPL 2008»
11 years 11 months ago
A note on harmonic subgraphs in labelled geometric graphs
Let S be a set of n points in general position in the plane, labelled bijectively with the integers {0, 1, . . ., n - 1}. Each edge (the straight segment that joins two points) is...
Gabriela Araujo, József Balogh, Ruy Fabila ...
COMPGEOM
2010
ACM
12 years 4 months ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
ENDM
2008
142views more  ENDM 2008»
11 years 12 months ago
Augmenting the Connectivity of Planar and Geometric Graphs
In this paper we study some connectivity augmentation problems. Given a connected graph G with some desirable property, we want to make G 2-vertex connected (or 2-edge connected) ...
Ignaz Rutter, Alexander Wolff
DIALM
2008
ACM
179views Algorithms» more  DIALM 2008»
12 years 1 months ago
Distance graphs: from random geometric graphs to Bernoulli graphs and between
A random geometric graph G(n, r) is a graph resulting from placing n points uniformly at random on the unit area disk, and connecting two points iff their Euclidean distance is at ...
Chen Avin
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