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121.
Enumeration of Maximum Acyclic Hypergraphs 总被引:1,自引:0,他引:1
Jian-fang Wang Hai-zhu LiInstitute of Applied Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2002,18(2):215-218
Abstract Acyclic hypergraphs are analogues of forests in graphs.They are very useful in the design ofdatabases. In this article,the maximum size of an acvclic hypergraph is determined and the number of maximumγ-uniform acyclic hypergraphs of order n is shown to be (_(r-1)~n)(n(r-1)-r~2 2r)~(n-r-1). 相似文献
122.
Let r be a fixed constant and let be an r‐uniform, D‐regular hypergraph on N vertices. Assume further that for some . Consider the random greedy algorithm for forming an independent set in . An independent set is chosen at random by iteratively choosing vertices at random to be in the independent set. At each step we chose a vertex uniformly at random from the collection of vertices that could be added to the independent set (i.e. the collection of vertices v with the property that v is not in the current independent set I and contains no edge in ). Note that this process terminates at a maximal subset of vertices with the property that this set contains no edge of ; that is, the process terminates at a maximal independent set. We prove that if satisfies certain degree and codegree conditions then there are vertices in the independent set produced by the random greedy algorithm with high probability. This result generalizes a lower bound on the number of steps in the H‐free process due to Bohman and Keevash and produces objects of interest in additive combinatorics. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 479–502, 2016 相似文献
123.
Oleg Pikhurko 《Graphs and Combinatorics》2008,24(4):391-404
For a k-graph F, let t l (n, m, F) be the smallest integer t such that every k-graph G on n vertices in which every l-set of vertices is included in at least t edges contains a collection of vertex-disjoint F-subgraphs covering all but at most m vertices of G. Let K m k denote the complete k-graph on m vertices. The function $t_{k-1} (kn, 0, K_k^k)For a k-graph F, let t
l
(n, m, F) be the smallest integer t such that every k-graph G on n vertices in which every l-set of vertices is included in at least t edges contains a collection of vertex-disjoint F-subgraphs covering all but at most m vertices of G. Let K
m
k
denote the complete k-graph on m vertices.
The function (i.e. when we want to guarantee a perfect matching) has been previously determined by Kühn and Osthus [9] (asymptotically)
and by R?dl, Ruciński, and Szemerédi [13] (exactly). Here we obtain asymptotic formulae for some other l. Namely, we prove that for any and ,
.
Also, we present various bounds in another special but interesting case: t
2(n, m, K
43) with m = 0 or m = o(n), that is, when we want to tile (almost) all vertices by copies of K
43, the complete 3-graph on 4 vertices.
Reverts to public domain 28 years from publication.
Oleg Pikhurko: Partially supported by the National Science Foundation, Grant DMS-0457512. 相似文献
124.
Yasuki Sekiguchi 《Operations Research Letters》1983,2(5):243-247
A facial structure of the node packing polytope, i.e., of the convex hull of integer solutions of the node packing problem, on hypergraphs is studied. First, the results extracted by Chvàtal and by Balas and Zemel on canonical facets of the node packing polytopes on graphs are generalized to derive some specific hypergraphs having canonical facets. Second, it is shown that the facial structure of the node packing polytope on a hypergraph, named a fat graph, has a very close relationship to the facial structures of the node packing polytope and also of the convex hull of integer solutions of an integer linear program, which are defined on a specific graph corresponding to the fat graph. 相似文献
125.
Counting acyclic hypergraphs 总被引:4,自引:0,他引:4
Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. The number of distinct
acyclic uniform hypergraphs withn labeled vertices is studied. With the aid of the principle of inclusion-exclusion, two formulas are presented. One is the
explicitformula for strict (d)-connected acyclic hypergraphs, the other is the recurrence formula for linear acyclic hypergraphs. 相似文献
126.
The Wiener index of a connected k-uniform hypergraph is defined as the summation of distances between all pairs of vertices. We determine the unique k-uniform unicyclic hypergraphs with maximum and second maximum, minimum and second minimum Wiener indices, respectively. 相似文献
127.
Let
$$\mathcal{H}$$ 相似文献
128.
129.
A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. We use to denote the 3-uniform hypergraph whose vertex set can be partitioned into two vertex classes and of size and , respectively, and whose edge set consists of all the triples containing at least two vertices of . Let be a 3-uniform hypergraph of order with no isolated vertex and for any two adjacent vertices . In this paper, we show that contains a matching of size if and only if is not a subgraph of . This result improves our previous one in Zhang and Lu (2018). 相似文献
130.
通过对帆船在海面上航行的受力情况及运动情况简要的分析,在风向保持不变,风速以及浪高满足函数变化时,建立在一定区域内如何逆风航行使得航行时间最少的目标函数,借助拉格朗日函数和欧拉方程,数值求解出最佳航行路线,对帆船运动员在实际操练中有一定指导意义. 相似文献