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math.CO2020
The threshold for the square of a Hamilton cycle
Jeff Kahn, Bhargav Narayanan, Jinyoung Park
Resolving a conjecture of Kühn and Osthus from 2012, we show that is the threshold for the random graph to contain the square of a Hamilton cycle.
math.CO2020
Tuza's Conjecture for random graphs
Jeff Kahn, Jinyoung Park
A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint t…