Perfect matchings in 3-partite 3-uniform hypergraphs
نویسندگان
چکیده
Let H be a 3-partite 3-uniform hypergraph with each partition class of size n, that is, a 3-uniform hypergraph such that every edge intersects every partition class in exactly one vertex. We determine the Dirac-type vertex degree thresholds for perfect matchings in 3-partite 3-uniform hypergraphs.
منابع مشابه
Matchings and Tilings in Hypergraphs
We consider two extremal problems in hypergraphs. First, given k ≥ 3 and k-partite k-uniform hypergraphs, as a generalization of graph (k = 2) matchings, we determine the partite minimum codegree threshold for matchings with at most one vertex left in each part, thereby answering a problem asked by Rödl and Ruciński. We further improve the partite minimum codegree conditions to sum of all k par...
متن کاملPerfect Fractional Matchings in $k$-Out Hypergraphs
Extending the notion of (random) k-out graphs, we consider when the k-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each r there is a k = k(r) such that the k-out r-uniform hypergraph on n vertices has a perfect fractional matching with high probability (i.e., with probability tending to 1 as n → ∞) and prove an analogous result for r-uniform r-...
متن کاملExact Minimum Degree Thresholds for Perfect Matchings in Uniform Hypergraphs Iii
We determine the exact minimum l-degree threshold for perfect matchings in k-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than 1 2 ( n k−l ) . This extends our previous results [18, 19] that determine the minimum l-degree thresholds for perfect matchings in k-uniform hypergraphs for all l ≥ k/2 and provides two new (exact) threshold...
متن کاملA Note on Perfect Matchings in Uniform Hypergraphs
We determine the exact minimum `-degree threshold for perfect matchings in kuniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than 12 ( n k−` ) . This extends our previous results that determine the minimum `-degree thresholds for perfect matchings in k-uniform hypergraphs for all ` > k/2 and provides two new (exact) thresholds: (k, `) =...
متن کاملApproximate Counting of Matchings in (3, 3)-Hypergraphs
We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as (3, 3)hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite (3, 3)-hypergraphs. The proof tech...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 127 شماره
صفحات -
تاریخ انتشار 2014