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WG
1999
Springer
14 years 8 days ago
Linear Orderings of Random Geometric Graphs
Abstract. In random geometric graphs, vertices are randomly distributed on [0, 1]2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layou...
Josep Díaz, Mathew D. Penrose, Jordi Petit,...
DM
2010
128views more  DM 2010»
13 years 8 months ago
Some remarks on the geodetic number of a graph
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimu...
Mitre Costa Dourado, Fábio Protti, Dieter R...
EJC
2010
13 years 8 months ago
Bandwidth, expansion, treewidth, separators and universality for bounded-degree graphs
We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an exp...
Julia Böttcher, Klaas P. Pruessmann, Anusch T...
DM
2008
177views more  DM 2008»
13 years 8 months ago
The independence number in graphs of maximum degree three
We prove that a K4-free graph G of order n, size m and maximum degree at most three has an independent set of cardinality at least 1 7 (4n - m - - tr) where counts the number of c...
Jochen Harant, Michael A. Henning, Dieter Rautenba...
COMGEO
2007
ACM
13 years 8 months ago
Drawings of planar graphs with few slopes and segments
We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-...
Vida Dujmovic, David Eppstein, Matthew Suderman, D...