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» The Alcuin Number of a Graph
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ISAAC
2009
Springer
87views Algorithms» more  ISAAC 2009»
14 years 13 days ago
Parameterizing Cut Sets in a Graph by the Number of Their Components
For a connected graph G = (V, E), a subset U ⊆ V is called a k-cut if U disconnects G, and the subgraph induced by U contains exactly k (≥ 1) components. More specifically, a ...
Takehiro Ito, Marcin Kaminski, Daniël Paulusm...
JGT
2010
158views more  JGT 2010»
13 years 6 months ago
Cubicity of interval graphs and the claw number
Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I1 × I2 × · · · × Ib, where ea...
Abhijin Adiga, L. Sunil Chandran
WG
2010
Springer
13 years 6 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...
SIAMDM
2010
130views more  SIAMDM 2010»
13 years 6 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...
APPML
2011
13 years 2 months ago
Bounds on the k-domination number of a graph
The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove t...
Ermelinda DeLaViña, Wayne Goddard, Michael ...