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On a rainbow version of Diracs theorem

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 نشر من قبل Jaehoon Kim
 تاريخ النشر 2019
  مجال البحث
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For a collection $mathbf{G}={G_1,dots, G_s}$ of not necessarily distinct graphs on the same vertex set $V$, a graph $H$ with vertices in $V$ is a $mathbf{G}$-transversal if there exists a bijection $phi:E(H)rightarrow [s]$ such that $ein E(G_{phi(e)})$ for all $ein E(H)$. We prove that for $|V|=sgeq 3$ and $delta(G_i)geq s/2$ for each $iin [s]$, there exists a $mathbf{G}$-transversal that is a Hamilton cycle. This confirms a conjecture of Aharoni. We also prove an analogous result for perfect matchings.



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