共查询到20条相似文献,搜索用时 15 毫秒
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Hans-Dietrich O. F. Gronau Martin Grüttmüller Sven Hartmann Uwe Leck Volker Leck 《Designs, Codes and Cryptography》2002,27(1-2):49-91
An orthogonal double cover (ODC) is a collection of n spanning subgraphs(pages) of the complete graph K
n such that they cover every edge of the completegraph twice and the intersection of any two of them contains exactly one edge. If all the pages are isomorphic tosome graph G, we speak of an ODC by G. ODCs have been studied for almost 25 years, and existenceresults have been derived for many graph classes. We present an overview of the current state of research alongwith some new results and generalizations. As will be obvious, progress made in the last 10 years is in many waysrelated to the work of Ron Mullin. So it is natural and with pleasure that we dedicate this article to Ron, on theoccasion of his 65th birthday. 相似文献
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令G为一具有n个节点的平面近三角剖分图,C为G的一个少圈二重覆盖(SCDC).本文首先给出了G的一些生成元,由此可以得到G的一个SCDC.若G为一外平面近三角剖分图,得到 |C|≤n-2的一充分必要条件;若 G至少有一个内点,得到|C|≤n-2的一充分条件. 相似文献
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A cover of a finite noncyclic group G is a family ? of proper subgroups of G whose union equals G. A cover of G is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite noncyclic groups all of whose irredundant covers are minimal. 相似文献
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Arthur Hoffmann-Ostenhof 《Graphs and Combinatorics》2013,29(4):977-979
The strong cycle double cover conjecture states that for every circuit C of a bridgeless cubic graph G, there is a cycle double cover of G which contains C. We conjecture that there is even a 5-cycle double cover S of G which contains C, i.e. C is a subgraph of one of the five 2-regular subgraphs of S. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of G. 相似文献
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Edita Máčajová André Raspaud Edita Rollová Martin Škoviera 《Journal of Graph Theory》2016,81(2):120-133
We introduce the concept of a signed circuit cover of a signed graph. A signed circuit cover is a natural analog of a circuit cover of a graph and is equivalent to a covering of the corresponding signed graphic matroid with circuits. As in the case of graphs, a signed graph has a signed circuit cover only when it admits a nowhere‐zero integer flow. In the present article, we establish the existence of a universal coefficient such that every signed graph G that admits a nowhere‐zero integer flow has a signed circuit cover of total length at most . We show that if G is bridgeless, then , and in the general case . 相似文献
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Mathematical Notes - 相似文献
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Let K be a discrete valuation field with ring of integers O K .Letf : X ! Y be a finite morphism of curves over K. In this article, we study some possible relationships between the models over O K of X and of Y. Three such relationships are listed below. Consider a Galois cover f : X ! Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-stable reduction over K,thenX achieves semi-stable reduction over some explicit tame extension of K.B/.WhenK is strictly henselian, we determine the minimal extension L=K with the property that X L has semi-stable reduction. Let f : X ! Y be a finite morphism, with g.Y/ > 2. We show that if X has a stable model X over O K ,thenY has a stable model Y over O K , and the morphism f extends to a morphism X ! Y. ! Y. Finally, given any finite morphism f : X ! Y, is it possible to choose suitable regular models X and Y of X and Y over O K such that f extends to a finite morphism X ! Y ?As wasshown by Abhyankar, the answer is negative in general. We present counterexamples in rather general situ-ations, with f a cyclic cover of any order > 4. On the other hand, we prove, without any hypotheses on the residual characteristic, that this extension problem has a positive solution when f is cyclic of order 2 or 3. 相似文献
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Generalized Petersen graphs are commonly used interconnection networks,and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel pro- cessing computer networks.In this paper,we show that the diameter and 3-wide diameter of generalized Petersen graph P (m,a) are both O( m 2a ),where a ≥ 3. 相似文献
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Vincenzo Di Gennaro 《Geometriae Dedicata》1998,71(1):91-96
We exhibit a simpler and quick proof of a theorem proved by G. Ellingsrud and Ch. Peskine, which states that there are only a finite number of components in the Hilbert scheme parametrizing smooth surfaces in P4 not of general type. 相似文献
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Let
be a hereditary torsion theory for the category
-mod of unital left
-modules over an associative ring
with an identity element. The purpose of this note is to prove that if the associated Gabriel filter
consists of finitely presented left ideals, then every module has a
-injective cover and if
contains a cofinal subset of finitely presented left ideals, then every module has a
-torsionfree
-injective cover. The methods used working with pure submodules contained in ``large" submodules also allow to unify the proofs of some previously known results. 相似文献
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设k≥2是一个整数。本文证明了任意有m条边的图都存在一个顶点的划分V_1,V_2…,V_k,使得e(V_1,V_2…,V_k)≥k-1/k m+k-1/2k((2m+1/4)~1/2-1/2)-(k-2)~2/8k,且max{e(V_i):1≤i≤k}≤m/k~2+(k-1)/2k~2((2m+1/4)~1/2-1/2+3/8-7k-4/8k~2.我们的结果改进了[Fan G.,Hou J.,Zeng Q.,A bound for judicious k-partitions of graphs,Discrete Appl.Math.,2014,179:86—99]的主要结论. 相似文献
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A transversal cover is a set of gk points in k disjoint groups of size g and a collection of b transversal subsets, called blocks, such that any pair of points not contained in the same group appears in at least one block. A central question is to determine, for given g, the minimum possible b for fixed k, or, alternatively, the maximum k for fixed b. The case g=2 was investigated and completely solved by Sperner sperner:28, Rényi renyi:71, Katona katona:73, and Kleitman and Spencer kleitman:73. For arbitrary g, asymptotic results are known but little is understood for small values of k. Constructions exist but these only produce upper bounds on b. The present article is concerned with lower bounds on b. We develop three general lower bounds on b for fixedg and k. The first one is proved using one of the principal constructions brett:97a, the second comes from the study of intersecting set-systems, and the third is shown by a set packing argument. In addition, we investigate upper bounds on k for small fixed b. This proves useful to reduce or eliminate the gap between lower and upper bounds on b for some transversal covers with small k. 相似文献
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Antonio Pasini 《Journal of Algebraic Combinatorics》2003,18(3):211-243
The geometries studied in this paper are obtained from buildings of spherical type by removing all chambers at non-maximal distance from a given element or flag. I consider a number of special cases of the above construction chosen among those which most frequently appear in the literature, proving that the resulting geometry is always simply connected but for three cases of small rank defined over GF(2) and GF(4). I also compute the universal cover in those exceptional cases. 相似文献
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本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间. 相似文献