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» Note on Sparse Random Graphs and Cover Graphs
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SODA
2004
ACM
144views Algorithms» more  SODA 2004»
13 years 6 months ago
Covering minimum spanning trees of random subgraphs
We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
Michel X. Goemans, Jan Vondrák
JCT
2007
108views more  JCT 2007»
13 years 5 months ago
The cover time of the preferential attachment graph
The preferential attachment graph Gm(n) is a random graph formed by adding a new vertex at each time step, with m edges which point to vertices selected at random with probability...
Colin Cooper, Alan M. Frieze
STOC
2002
ACM
121views Algorithms» more  STOC 2002»
14 years 5 months ago
Almost all graphs with average degree 4 are 3-colorable
We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable a...
Dimitris Achlioptas, Cristopher Moore
ALGORITHMICA
2010
147views more  ALGORITHMICA 2010»
13 years 5 months ago
Note on the Structure of Kruskal's Algorithm
We study the merging process when Kruskal's algorithm is run with random graphs as inputs. Our aim is to analyze this process when the underlying graph is the complete graph ...
Nicolas Broutin, Luc Devroye, Erin McLeish