Pairwise disjoint maximal cliques in random graphs and sequential motion planning on random right angled Artin groups
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The clique number of a random graph in the Erdös–Rényi model [Formula: see text] yields a random variable which takes values asymptotically almost surely (as [Formula: see text]) within one of an explicit logarithmic function [Formula: see text]. We show that random graphs have, asymptotically almost surely, arbitrarily many pairwise disjoint cliques with [Formula: see text] vertices. Such a result is motivated by, and applied to, the multi-tasking version of Farber’s topological model to study the motion planning problem in robotics. Indeed, we study the behavior of all the higher topological complexities of Eilenberg–MacLane spaces of type [Formula: see text], where [Formula: see text] is a random right angled Artin group.
2011 ◽
Vol 03
(01)
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pp. 69-87
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2011 ◽
Vol 20
(5)
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pp. 763-775
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2018 ◽
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2009 ◽
Vol 82
(8)
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pp. 1539-1563
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