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给出了ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠的定义,讨论了ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠的优美性,用构造性的方法给出了图ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠的四种优美标号,并证明了这些ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠也是交错图. 相似文献
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Kite-可分组设计的相交数问题是确定所有可能的元素对$(T,s)$, 使得存在一对具有相同组型 $T$ 的Kite-可分组设计 $(X,{\cal H},{\cal B}_1)$ 和$(X,{\cal H},{\cal B}_2)$ 满足$|{\cal B}_1\cap {\cal B}_2|=s$. 本文研究组型为 $2^u$ 的Kite-可分组设计的相交数问题, 设 $J(u)=\{s:\exists$ 组型为 $2^u$ 的Kite-可分组设计相交于$s$ 个区组\}, $I(u)=\{0,1,\ldots,b_{u}-2,b_{u}\}$,其中 $b_u=u(u-1)/2$ 是组型为$2^u$ 的Kite-可分组设计的区组个数. 我们将给出对任意整数 $u\ge 4$ 都有$J(u)=I(u)$ 且 $J(3)= \{0,3\}$. 相似文献
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证明了:对任一在Cn中超球Bn上可微的(0,q)式g(z)若适合(-e)g=0,而且g在Bn内有紧致的支集,则当n≥q+1时v(w)=(-e)*∫Bng(z)∧*z—N(z,w)是(-e)方程(-e)v=g之解,它在边界Bn上为零. 相似文献
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证明了:对任一在Cn中超球Bn上可微的(0,q)式g(z)若适合g=0,而且g在Bn内有紧致的支集,则当n≥q 1时v(w)=*∫Bng(z)∧*zN(z,w)是方程v=g之解,它在边界Bn上为零. 相似文献
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证明了图2Kv的可旋转(4,6)圈系存在的充分必要条件为:v≥10,v≡0,5(mod 10). 相似文献
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The honeymoon Oberwolfach problem HOP asks the following question. Given newlywed couples at a conference and round tables of sizes , is it possible to arrange the participants at these tables for meals so that each participant sits next to their spouse at every meal and sits next to every other participant exactly once? A solution to HOP is a decomposition of , the complete graph with additional copies of a fixed 1‐factor , into 2‐factors, each consisting of disjoint ‐alternating cycles of lengths . It is also equivalent to a semi‐uniform 1‐factorization of of type ; that is, a 1‐factorization such that for all , the 2‐factor consists of disjoint cycles of lengths . In this paper, we first introduce the honeymoon Oberwolfach problem and then present several results. Most notably, we completely solve the case with uniform cycle lengths, that is, HOP. In addition, we show that HOP has a solution in each of the following cases: ; is odd and ; as well as for all . We also show that HOP has a solution whenever is odd and the Oberwolfach problem with tables of sizes has a solution. 相似文献
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Let n > 1 be an integer and let a2,a3,…,an be nonnegative integers such that . Then can be factored into ‐factors, ‐factors,…, ‐factors, plus a 1‐factor. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 151–161, 2002 相似文献
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Simone Costa 《组合设计杂志》2020,28(5):366-383
Let F be a 2‐regular graph of order v. The Oberwolfach problem, OP(F), asks for a 2‐factorization of the complete graph on v vertices in which each 2‐factor is isomorphic to F. In this paper, we give a complete solution to the Oberwolfach problem over infinite complete graphs, proving the existence of solutions that are regular under the action of a given involution free group G. We will also consider the same problem in the more general context of graphs F that are spanning subgraphs of an infinite complete graph and we provide a solution when F is locally finite. Moreover, we characterize the infinite subgraphs L of F such that there exists a solution to OP(F) containing a solution to OP(L). 相似文献
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Let n3 and let F be a 2-regular graph of order n. The Oberwolfach problem OP(F) asks for a 2-factorisation of Kn if n is odd, or of Kn−I if n is even, in which each 2-factor is isomorphic to F. We show that there is an infinite set of primes congruent to such that OP(F) has a solution for any 2-regular graph F of order . We also show that for each of the infinitely many with prime, OP(F) has a solution for any 2-regular graph F of order n. 相似文献
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We consider k‐factorizations of the complete graph that are 1‐rotational under an assigned group G, namely that admit G as an automorphism group acting sharply transitively on all but one vertex. After proving that the k‐factors of such a factorization are pairwise isomorphic, we focus our attention to the special case of k = 2, a case in which we prove that the involutions of G necessarily form a unique conjugacy class. We completely characterize, in particular, the 2‐factorizations that are 1‐rotational under a dihedral group. Finally, we get infinite new classes of previously unknown solutions to the Oberwolfach problem via some direct and recursive constructions. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 87–100, 2008 相似文献
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It is shown that if F1, F2, …, Ft are bipartite 2‐regular graphs of order n and α1, α2, …, αt are positive integers such that α1 + α2 + ? + αt = (n ? 2)/2, α1≥3 is odd, and αi is even for i = 2, 3, …, t, then there exists a 2‐factorization of Kn ? I in which there are exactly αi 2‐factors isomorphic to Fi for i = 1, 2, …, t. This result completes the solution of the Oberwolfach problem for bipartite 2‐factors. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:22‐37, 2011 相似文献
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Every 1‐rotational solution of a classic or twofold Oberwolfach problem (OP) of order n is generated by a suitable 2‐factor (starter) of or , respectively. It is shown that any starter of a twofold OP of order n gives rise to a starter of a classic OP of order (doubling construction). It is also shown that by suitably modifying the starter of a classic OP, one may obtain starters of some other OPs of the same order but having different parameters. The combination of these two constructions leads to lots of new infinite classes of solvable OPs. Still more classes can be obtained with the help of a third construction making use of the possible gracefulness of a graph whose connected components are cycles and at most one path. As one of the many applications, Hilton and Johnson's [J London Math Soc, 64 (2001) 513–522] bound about the solvability of OP is improved to in the case of r even. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 483‐503, 2012 相似文献
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Let v be a positive integer and let K be a set of positive integers. A (v, K, 1)-Mendelsohn design, which we denote briefly by (v, K, 1)-MD, is a pair (X, B) where X is a v-set (of points) and B is a collection of cyclically ordered subsets of X (called blocks) with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t =1, 2,..., r, every ordered pair of points of X are t-apart in exactly one block of B, then the (v, K, 1)-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect (v, K, 1)-MD. If K = {k) and r = k - 1, then an r-fold perfect (v, (k), 1)-MD is essentially the more familiar (v, k, 1)-perfect Mendelsohn design, which is briefly denoted by (v, k, 1)-PMD. In this paper, we investigate the existence of 4-fold perfect (v, (5, 8}, 1)-Mendelsohn designs. 相似文献
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Constraints are given on graceful labellings for paths that allow them to be used to construct cyclic solutions to the Oberwolfach Problem. We give examples of graceful labellings meeting these constraints and hence, infinitely many new families of cyclic solutions can be constructed. 相似文献
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We prove that , the complete graph of even order with a 1‐factor duplicated, admits a decomposition into 2‐factors, each a disjoint union of cycles of length if and only if , except possibly when is odd and . In addition, we show that admits a decomposition into 2‐factors, each a disjoint union of cycles of lengths , whenever are all even. 相似文献