»ã±¨±êÌâ (Title)£ºCo-degree threshold for rainbow perfect matchings in uniform hypergraphs£¨¹ØÓÚÒ»Ö³¬Í¼ÉÏÓвÊÉ«ÃÀÂúÆ¥ÅäµÄÓà¶ÈãÐÖµÎÊÌ⣩

»ã±¨ÈË (Speaker)£ºÂ³ºìÁÁ ½ÌÊÚ£¨Î÷°²½»Í¨´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê9ÔÂ21ÈÕ(ÖÜËÄ) 14:30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿D204¡¢ÌÚѶ»áÒéºÅ546 972 901

Ô¼ÇëÈË(Inviter)£ºÑîٻٻ

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»ã±¨ÌáÒª£º Let k and n be two integers, with k\geq 3, n\equiv 0\pmod k, and n sufficiently large. We determine the (k-1)-degree threshold for the existence of a rainbow perfect matchings in n-vertex k-uniform hypergraph. This implies the result of R\"odl, Ruci\'nski, and Szemer\'edi on the (k-1)-degree threshold for the existence of perfect matchings in n-vertex k-uniform hypergraphs. In our proof, we identify the extremal configurations of closeness, and consider whether or not the hypergraph is close to the extremal configuration. In addition, we also develop a novel absorbing device and generalize the absorbing lemma of R\"odl, Ruci\'nski, and Szemer\'edi. This is joint work with Yan Wang and Xingxing Yu.