共查询到19条相似文献,搜索用时 46 毫秒
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基于王建方和李东给出的超图哈密顿圈的定义和Katona-Kierstead给出的超图哈密顿链的定义,近年来,国内外学者对一致超图的哈密顿圈分解的研究有一系列结果.特别是Bailey-Stevens和Meszka-Rosa研究了完全3-一致超图K_n~((3))的哈密顿圈分解,得到了n=6k+1,6k+2(k=1,2,3,4,5)的哈密顿圈分解.本文在吉日木图提出的边划分方法的基础上继续研究,得到了完全3-一致超图K_n~((3))的哈密顿圈分解的算法,由此得到了n=6k+2,6k+4(k=1,2,3,4,5,6,7),n=6k+5(k=1,2,3,4,5,6)时的圈分解.这一结果将Meszka-Rosa关于K_n~((3))的哈密顿圈分解结果从n≤32提高到了n≤46(n≠43). 相似文献
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假设c是一个小于1/1152的常数,证明:对于每个充分大的偶数n,如果一个具有n个顶点的3一致完全超图的边着色满足每种颜色出现的次数不超过[cn],那么必含有一个每条边颜色都不一样的彩色哈密顿圈。 相似文献
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设H=(V,E)是以V为顶点集, E为(超)边集的超图. 如果H的每条边均含有k个顶点, 则称H是k-一致超图. 超图H的点子集T称为它的一个横贯, 如果T 与H 的每条边均相交. 超图H的全横贯是指它的一个横贯T, 并且T还满足如下性质: T中每个顶点均至少有一个邻点在T中. H 的全横贯数定义为H 的最小全横贯所含顶点的数目, 记作\tau_{t}(H). 对于整数k\geq 2, 令b_{k}=\sup_{H\in{\mathscr{H}}_{k}}\frac{\tau_{t}(H)}{n_{H}+m_{H}}, 其中n_H=|V|, m_H=|E|, {\mathscr{H}}_{k} 表示无孤立点和孤立边以及多重边的k-一致超图类. 最近, Bujt\'as和Henning等证明了如下结果: b_{2}=\frac{2}{5}, b_{3}=\frac{1}{3}, b_{4}=\frac{2}{7}; 当k\geq 5 时, 有b_{k}\leq \frac{2}{7}以及b_{6}\leq \frac{1}{4}; 当k\geq 7 时, b_{k}\leq \frac{2}{9}. 证明了对5-一致超图, b_{5}\leq \frac{4}{15}, 从而改进了当k=5 时b_k的上界. 相似文献
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主要讨论了不含k-C-圈的n阶r-一致超图,对不同的k,分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件. 相似文献
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王殿军 《高校应用数学学报(A辑)》1993,(4):425-429
本文给出完全图圈分解的一种新方法,设Kn(n≥3)是一个n阶完全图,我们得到下列结果:(1)若n为奇数,G是n阶群,并且{o(x)│∈G,o(x)≥3}={a1,…,at},则Kn=m1Ca1+…+mtCat。(2)若n为偶数,G是n阶群,T={x│x∈G,o(x)=2}={x0,x1,y1,…,xs,ys},o(xiyi)=bi,i=1,…,s及{o(x)│x∈G,o(x)≥}={a1,…,at 相似文献
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Large Sets of Wrapped K–K Hamilton Cycle Decompositions of Complete Bipartite 3‐Uniform Hypergraphs 下载免费PDF全文
Using the Katona–Kierstead (K–K) definition of a Hamilton cycle in a uniform hypergraph, we investigate the existence of wrapped K–K Hamilton cycle decompositions of the complete bipartite 3‐uniform hypergraph and their large sets, settling their existence whenever n is prime. 相似文献
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If a graph G decomposes into edge‐disjoint 4‐cycles, then each vertex of G has even degree and 4 divides the number of edges in G. It is shown that these obvious necessary conditions are also sufficient when G is any simple graph having minimum degree at least , where n is the number of vertices in G. This improves the bound given by Gustavsson (PhD Thesis, University of Stockholm, 1991), who showed (as part of a more general result) sufficiency for simple graphs with minimum degree at least . On the other hand, it is known that for arbitrarily large values of n there exist simple graphs satisfying the obvious necessary conditions, having n vertices and minimum degree , but having no decomposition into edge‐disjoint 4‐cycles. We also show that if G is a bipartite simple graph with n vertices in each part, then the obvious necessary conditions for G to decompose into 4‐cycles are sufficient when G has minimum degree at least . 相似文献
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Decomposing Complete Equipartite Multigraphs into Cycles of Variable Lengths: The Amalgamation‐detachment Approach 下载免费PDF全文
Using the technique of amalgamation‐detachment, we show that the complete equipartite multigraph can be decomposed into cycles of lengths (plus a 1‐factor if the degree is odd) whenever there exists a decomposition of into cycles of lengths (plus a 1‐factor if the degree is odd). In addition, we give sufficient conditions for the existence of some other, related cycle decompositions of the complete equipartite multigraph . 相似文献
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A 3‐uniform friendship hypergraph is a 3‐uniform hypergraph in which, for all triples of vertices x, y, z there exists a unique vertex w, such that , and are edges in the hypergraph. Sós showed that such 3‐uniform friendship hypergraphs on n vertices exist with a so‐called universal friend if and only if a Steiner triple system, exists. Hartke and Vandenbussche used integer programming to search for 3‐uniform friendship hypergraphs without a universal friend and found one on 8, three nonisomorphic on 16 and one on 32 vertices. So far, these five hypergraphs are the only known 3‐uniform friendship hypergraphs. In this paper we construct an infinite family of 3‐uniform friendship hypergraphs on 2k vertices and edges. We also construct 3‐uniform friendship hypergraphs on 20 and 28 vertices using a computer. Furthermore, we define r‐uniform friendship hypergraphs and state that the existence of those with a universal friend is dependent on the existence of a Steiner system, . As a result hereof, we know infinitely many 4‐uniform friendship hypergraphs with a universal friend. Finally we show how to construct a 4‐uniform friendship hypergraph on 9 vertices and with no universal friend. 相似文献
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研究了一般的标号严格(d)-连通无圈超图的计数,得到了n阶标号严格(d)-连通无圈超图的计数公式. 相似文献
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Marián Trenkler 《Graphs and Combinatorics》2001,17(1):171-175
We deal with complete k-partite hypergraphs and we show that for all k≥2 and n≠2,6 its hyperedges can be labeled by consecutive integers 1,2,…,n
k
such that the sum of labels of the hyperedges incident to (k−1) particular vertices is the same for all (k−1)-tuples of vertices from (k−1) independent sets.
Received: December 8, 1997 Final version received: July 26, 1999 相似文献
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Let 2 ≤q ≤min{p, t − 1} be fixed and n → ∞. Suppose that
is a p-uniform hypergraph on n vertices that contains no complete q-uniform hypergraph on t vertices as a trace. We determine the asymptotic maximum size of
in many cases. For example, when q = 2 and p∈{t, t + 1}, the maximum is
, and when p = t = 3, it is
for all n≥ 3. Our proofs use the Kruskal-Katona theorem, an extension of the sunflower lemma due to Füredi, and recent results on hypergraph
Turán numbers.
Research supported in part by NSF grants DMS-0400812 and an Alfred P. Sloan Research Fellowship.
Research supported in part by NSA grant H98230-06-1-0140. Part of the research conducted while his working at University of
Illinois at Chicago as a NSF VIGRE postdot. 相似文献
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Raphael Yuster 《Combinatorica》2000,20(1):119-140
T be a simple k-uniform hypertree with t edges. It is shown that if H is any k-uniform hypergraph with n vertices and with minimum degree at least , and the number of edges of H is a multiple of t then H has a T-decomposition. This result is asymptotically best possible for all simple hypertrees with at least two edges. Received December 28, 1998 相似文献