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» On the hyperbolicity constant in graphs
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STOC
2002
ACM
121views Algorithms» more  STOC 2002»
14 years 7 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
CORR
2012
Springer
194views Education» more  CORR 2012»
12 years 3 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»
11 years 9 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»
13 years 7 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
13 years 8 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...