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Award ID contains: 2054503

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  1. ; ; (, ACM)
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  2. ; (, The Electronic Journal of Combinatorics)
    Let $$N=\binom{n}{2}$$ and $$s\geq 2$$. Let $$e_{i,j},\,i=1,2,\ldots,N,\,j=1,2,\ldots,s$$ be $$s$$ independent permutations of the edges $$E(K_n)$$ of the complete graph $$K_n$$. A MultiTree is a set $$I\subseteq [N]$$ such that the edge sets $$E_{I,j}$$ induce spanning trees for $$j=1,2,\ldots,s$$. In this paper we study the following question: what is the smallest $m=m(n)$ such that w.h.p. $[m]$ contains a MultiTree. We prove a hitting time result for $s=2$ and an $$O(n\log n)$$ bound for $$s\geq 3$$. 
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  3. ; (, Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA))
    Accepted Manuscript Full Text Available
  4. ; ; ; ; ; ; ; ; ; (, Journal of Theoretical Biology)
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  5. ; (, Discrete Applied Mathematics)
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