60 search results - page 1 / 12 » On embeddability and stresses of graphs |
COMBINATORICA
2007
13 years 5 months ago
2007
Gluck [6] has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K5-minor freeness gua...
JCT
2008
13 years 5 months ago
2008
Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these invest...
SODA
2010
ACM
14 years 2 months ago
2010
ACM
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation al...
GD
2009
Springer
13 years 10 months ago
2009
Springer
In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains o...
GC
2007
Springer
13 years 5 months ago
2007
Springer
Let G be a connected graph of order n and girth g. If dG(u) + dG(v) ≥ n − 2g + 5 for any two non-adjacent vertices u and v, then G is up-embeddable. Further more, the lower bou...