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CPC
2007
95views more  CPC 2007»
15 years 6 months ago
Colouring Random Regular Graphs
In a previous paper we showed that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6-regular...
Lingsheng Shi, Nicholas C. Wormald
CPC
2007
112views more  CPC 2007»
15 years 6 months ago
Graphs with Large Girth Not Embeddable in the Sphere
In 1972, M. Rosenfeld asked if every triangle-free graph could be embedded in the unit sphere Sd in such a way that two vertices joined by an edge have distance more than √ 3 (i...
Pierre Charbit, Stéphan Thomassé
SIAMDM
2008
79views more  SIAMDM 2008»
15 years 6 months ago
Reconfigurations in Graphs and Grids
Let G be a connected graph, and let V and V two n-element subsets of its vertex set V (G). Imagine that we place a chip at each element of V and we want to move them into the posi...
Gruia Calinescu, Adrian Dumitrescu, János P...
SIAMDM
2010
130views more  SIAMDM 2010»
15 years 4 months ago
On the Hull Number of Triangle-Free Graphs
A set of vertices C in a graph is convex if it contains all vertices which lie on shortest paths between vertices in C. The convex hull of a set of vertices S is the smallest conve...
Mitre Costa Dourado, Fábio Protti, Dieter R...
WG
2010
Springer
15 years 4 months ago
Graphs with Large Obstacle Numbers
Motivated by questions in computer vision and sensor networks, Alpert et al. [3] introduced the following definitions. Given a graph G, an obstacle representation of G is a set of...
Padmini Mukkamala, János Pach, Deniz Sari&o...