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» Packing Cliques in Graphs with Independence Number 2
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COMBINATORICA
2011
12 years 7 months ago
On the chromatic number of random geometric graphs
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...
Colin McDiarmid, Tobias Müller
IPL
2007
94views more  IPL 2007»
13 years 7 months ago
A note on the Hadwiger number of circular arc graphs
Abstract. The intention of this note is to motivate the researchers to study Hadwiger’s conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G...
N. S. Narayanaswamy, Naveen Belkale, L. Sunil Chan...
JGT
2006
40views more  JGT 2006»
13 years 7 months ago
How many graphs are unions of k-cliques?
We study the number F[n; k] of n-vertex graphs that can be written as the edgeunion of k-vertex cliques. We obtain reasonably tight estimates for F[n; k] in the cases (i) k = n-o(...
Béla Bollobás, Graham Brightwell
DAGSTUHL
2004
13 years 9 months ago
Finding Isolated Cliques by Queries -- An Approach to Fault Diagnosis with Many Faults
A well-studied problem in fault diagnosis is to identify the set of all good processors in a given set {p1, p2, . . . , pn} of processors via asking some processors pi to test whet...
William I. Gasarch, Frank Stephan
JGT
2007
130views more  JGT 2007»
13 years 7 months ago
Vertex partitions and maximum degenerate subgraphs
: Let G be a graph with maximum degree d ≥ 3 and ω(G) ≤ d, where ω(G) is the clique number of the graph G. Let p1 and p2 be two positive integers such that d = p1 + p2. In th...
Martín Matamala