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» On the hyperbolicity constant in graphs
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STOC
2002
ACM
121views Algorithms» more  STOC 2002»
16 years 57 min 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
CORR
2012
Springer
194views Education» more  CORR 2012»
13 years 7 months ago
A Graph Theoretical Approach to Network Encoding Complexity
Consider an acyclic directed network G with sources S1, S2, . . . , Sl and distinct sinks R1, R2, . . . , Rl. For i = 1, 2, . . . , l, let ci denote the min-cut between Si and Ri....
Li Xu, Weiping Shang, Guangyue Han
SODA
2012
ACM
205views Algorithms» more  SODA 2012»
13 years 2 months ago
Global minimum cuts in surface embedded graphs
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g,...
Jeff Erickson, Kyle Fox, Amir Nayyeri
DM
1998
73views more  DM 1998»
14 years 11 months ago
On constructing snakes in powers of complete graphs
We prove the conjecture of Abbott and Katchalski that for every m ≥ 2 there is a positive constant λm such that S(Kd mn) ≥ λmnd−1 S(Kd−1 m ) where S(Kd m) is the length o...
Jerzy Wojciechowski
CCCG
2010
15 years 1 months ago
3d local algorithm for dominating sets of unit disk graphs
A dominating set of a graph G = (V, E) is a subset V V of the nodes such that for all nodes v V , either v V or a neighbor u of v is in V . Several routing protocols in ad hoc ...
Alaa Eddien Abdallah, Thomas Fevens, Jaroslav Opat...