Large Cliques in a Power-Law Random Graph
2010 ◽
Vol 47
(04)
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pp. 1124-1135
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In this paper we study the size of the largest clique ω(G(n, α)) in a random graph G(n, α) on n vertices which has power-law degree distribution with exponent α. We show that, for ‘flat’ degree sequences with α > 2, with high probability, the largest clique in G(n, α) is of a constant size, while, for the heavy tail distribution, when 0 < α < 2, ω(G(n, α)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, α) a large clique of size (1 − o(1))ω(G(n, α)) in polynomial time.
2010 ◽
Vol 47
(4)
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pp. 1124-1135
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Keyword(s):
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2013 ◽
Vol 2013
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pp. 1-12
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Keyword(s):
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2008 ◽
Vol 18
(4)
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pp. 1651-1668
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Keyword(s):
2019 ◽
Vol 56
(3)
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pp. 672-700
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