共查询到20条相似文献,搜索用时 15 毫秒
1.
Darryn Bryant 《组合设计杂志》2004,12(2):147-155
For all integers n ≥ 5, it is shown that the graph obtained from the n‐cycle by joining vertices at distance 2 has a 2‐factorization is which one 2‐factor is a Hamilton cycle, and the other is isomorphic to any given 2‐regular graph of order n. This result is used to prove several results on 2‐factorizations of the complete graph Kn of order n. For example, it is shown that for all odd n ≥ 11, Kn has a 2‐factorization in which three of the 2‐factors are isomorphic to any three given 2‐regular graphs of order n, and the remaining 2‐factors are Hamilton cycles. For any two given 2‐regular graphs of even order n, the corresponding result is proved for the graph Kn ‐ I obtained from the complete graph by removing the edges of a 1‐factor. © 2004 Wiley Periodicals, Inc. 相似文献
2.
Let n≥2 be an integer. The complete graph Kn with a 1‐factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn−F has a decomposition into Hamilton cycles which are symmetric with respect to the 1‐factor F if and only if n≡2, 4 mod 8. We also show that the complete bipartite graph Kn, n has a symmetric Hamilton cycle decomposition if and only if n is even, and that if F is a 1‐factor of Kn, n, then Kn, n−F has a symmetric Hamilton cycle decomposition if and only if n is odd. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:1‐15, 2010 相似文献
3.
Marco Buratti 《组合设计杂志》2003,11(6):433-441
We give an explicit solution to the existence problem for 1‐rotational k‐cycle systems of order v < 3k with k odd and v ≠ 2k + 1. We also exhibit a 2‐rotational k‐cycle system of order 2k + 1 for any odd k. Thus, for k odd and any admissible v < 3k there exists a 2‐rotational k‐cycle system of order v. This may also be viewed as an alternative proof that the obvious necessary conditions for the existence of odd cycle systems are also sufficient. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 433–441, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10061 相似文献
4.
We construct a new symmetric Hamilton cycle decomposition of the complete graph Kn for odd n > 7. © 2003 Wiley Periodicals, Inc. 相似文献
5.
Given two 2‐regular graphs F1 and F2, both of order n, the Hamilton‐Waterloo Problem for F1 and F2 asks for a factorization of the complete graph into α1 copies of F1, α2 copies of F2, and a 1‐factor if n is even, for all nonnegative integers α1 and α2 satisfying . We settle the Hamilton‐Waterloo Problem for all bipartite 2‐regular graphs F1 and F2 where F1 can be obtained from F2 by replacing each cycle with a bipartite 2‐regular graph of the same order. 相似文献
6.
The Hamilton–Waterloo problem asks for a 2‐factorization of (for v odd) or minus a 1‐factor (for v even) into ‐factors and ‐factors. We completely solve the Hamilton–Waterloo problem in the case of C3‐factors and ‐factors for . 相似文献
7.
We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005 相似文献
8.
Hongtao Zhao 《Discrete Mathematics》2008,308(21):4931-4940
The existence spectrums for large sets of Hamilton cycle decompositions and Hamilton path decompositions are completed. Also, we show that the completion of large sets of directed Hamilton cycle decompositions and directed Hamilton path decompositions depends on the existence of certain special tuscan squares. Several conjectures about special tuscan squares are posed. 相似文献
9.
In this article, we consider the Hamilton‐Waterloo problem for the case of Hamilton cycles and triangle‐factors when the order of the complete graph Kn is even. We completely solved the problem for the case n≡24 (mod 36). For the cases n≡0 (mod 18) and n≡6 (mod 36), we gave an almost complete solution. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 305–316, 2012 相似文献
10.
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
11.
The necessary and sufficient conditions for the existence of a 1‐rotational k‐cycle system of the complete graph Kv are established. The proof provides an algorithm able to determine, directly and explicitly, an odd k‐cycle system of Kv whenever such a system exists. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 283–293, 2009 相似文献
12.
For all odd integers n ≥ 1, let Gn denote the complete graph of order n, and for all even integers n ≥ 2 let Gn denote the complete graph of order n with the edges of a 1‐factor removed. It is shown that for all non‐negative integers h and t and all positive integers n, Gn can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in Gn. © 2004 Wiley Periodicals, Inc. 相似文献
13.
《Journal of Graph Theory》2018,88(3):434-448
The natural infinite analog of a (finite) Hamilton cycle is a two‐way‐infinite Hamilton path (connected spanning 2‐valent subgraph). Although it is known that every connected 2k‐valent infinite circulant graph has a two‐way‐infinite Hamilton path, there exist many such graphs that do not have a decomposition into k edge‐disjoint two‐way‐infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every 2k‐valent connected circulant graph has a decomposition into k edge‐disjoint Hamilton cycles. We settle the problem of decomposing 2k‐valent infinite circulant graphs into k edge‐disjoint two‐way‐infinite Hamilton paths for , in many cases when , and in many other cases including where the connection set is or . 相似文献
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15.
R.S. Manikandan 《Discrete Mathematics》2008,308(16):3586-3606
In this paper, tensor product of two regular complete multipartite graphs is shown to be Hamilton cycle decomposable. Using this result, it is immediate that the tensor product of two complete graphs with at least three vertices is Hamilton cycle decomposable thereby providing an alternate proof of this fact. 相似文献
16.
A. V. Pyatkin 《Journal of Graph Theory》2002,41(4):286-291
P. Erd?s conjectured in [2] that r‐regular 4‐critical graphs exist for every r ≥ 3 and noted that no such graphs are known for r ≥ 6. This article contains the first example of a 6‐regular 4‐critical graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 286–291, 2002 相似文献
17.
We consider the existence of several different kinds of factors in 4‐connected claw‐free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4‐connected line graph is hamiltonian, i.e., has a connected 2‐factor. Conjecture 2 (Matthews and Sumner): Every 4‐connected claw‐free graph is hamiltonian. We first show that Conjecture 2 is true within the class of hourglass‐free graphs, i.e., graphs that do not contain an induced subgraph isomorphic to two triangles meeting in exactly one vertex. Next we show that a weaker form of Conjecture 2 is true, in which the conclusion is replaced by the conclusion that there exists a connected spanning subgraph in which each vertex has degree two or four. Finally we show that Conjectures 1 and 2 are equivalent to seemingly weaker conjectures in which the conclusion is replaced by the conclusion that there exists a spanning subgraph consisting of a bounded number of paths © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 125–136, 2001 相似文献
18.
A large set of CS(v, k, λ), k‐cycle system of order v with index λ, is a partition of all k‐cycles of Kv into CS(v, k, λ)s, denoted by LCS(v, k, λ). A (v ? 1)‐cycle is called almost Hamilton. The completion of the existence spectrum for LCS(v, v ? 1, λ) only depends on one case: all v ≥ 4 for λ = 2. In this article, it is shown that there exists an LCS(v, v ? 1,2) for any v ≡ 0,1 (mod 4) except v = 5, and for v = 6,7,10,11. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 53–69, 2008 相似文献
19.
For k = 1 and k = 2, we prove that the obvious necessary numerical conditions for packing t pairwise edge‐disjoint k‐regular subgraphs of specified orders m1,m2,… ,mt in the complete graph of order n are also sufficient. To do so, we present an edge‐coloring technique which also yields new proofs of various known results on graph factorizations. For example, a new construction for Hamilton cycle decompositions of complete graphs is given. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 499–506, 2008 相似文献
20.
We show via an exhaustive computer search that there does not exist a (K6?e)‐decomposition of K29. This is the first example of a non‐complete graph G for which a G‐decomposition of K2|E(G)|+1 does not exist. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 94–104, 2010 相似文献