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1.
Guantao Chen Ronald J. Gould Michael S. Jacobson Richard H. Schelp 《Journal of Graph Theory》1994,18(7):663-672
For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a bound on the smallest number of cycles in G containing all the vertices of G. We show that if for all x, y ? V(G), |N(x) ∩ N(y)| ≧ 2n/5 + 1, then V(G) is coverable by at most two cycles. Several related results and extensions to t cycles are also given. 相似文献
2.
An (n, j) linear forest L is the disjoint union of nontrivial paths, such that j of the paths have an odd number of vertices and the union has n vertices. For L, an (n1.j1) linear forest and l2 an (n.j1) linear forest, we show that This answers in the affirmative a conjecture of Burr and Roberts. 相似文献
3.
We introduce a closure concept in the class of line graphs and claw‐free graphs based on contractibility of certain subgraphs in the line graph preimage. The closure can be considered as a common generalization and strengthening of the reduction techniques of Catlin and Veldman and of the closure concept introduced by the first author. We show that the closure is uniquely determined and the closure operation preserves the circumference of the graph. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 37–48, 2003 相似文献
4.
A formula is found for the maximum number of edges in a graph G ? K(a, b) which contains no path P2l for l > c. A similar formula is found for the maximum number of edges in G ? K(a, b) containing no P2l + 1 for l > c. In addition, all extremal graphs are determined. 相似文献
5.
A graph G is co-connected if both G and its complement ? are connected and nontrivial. For two graphs A and B, the connected Ramsey number rc(A, B) is the smallest integer n such that there exists a co-connected graph of order n, and if G is a co-connected graph on at least n vertices, then A ? G or B ? ?. If neither A or B contains a bridge, then it is known that rc(A, B) = r(A, B), where r(A, B) denotes the usual Ramsey number of A and B. In this paper rc(A, B) is calculated for some pairs (A, B) when r(A, B) is known and at least one of the graphs A or B has a bridge. In particular, rc(A, B) is calculated for A a path and B either a cycle, star, or complete graph, and for A a star and B a complete graph. 相似文献
6.
M.A. Corrêa F. Bohn A.D.C. Viegas M.A. Carara L.F. Schelp R.L. Sommer 《Journal of magnetism and magnetic materials》2008,320(14):e25-e28
We study the magnetic properties at high frequency of new structures of the tri-layer samples. The magnetoimpedance effect was analyzed in FM/i/Cu/i/FM sandwiched layers, where the ferromagnetic layer (FM) is, in fact, a multilayered film [F (10 nm)+Cu (1 nm)]×50 and F is the amorphous ferromagnetic alloy Fe73.5Cu1Nb3Si13.5B9 and i is an isolating layer produced by magnetron sputtering. The effect of, both, the probe current frequency (in the range 10 MHz–1.8 GHz) and the dimensions of the magnetic and non-magnetic layers of the MI response were investigated. A comparison between samples with and without the isolating layer is discussed. MI ratios of 220% were obtained for samples at 180 MHz with a ferromagnetic and Cu width layers of 2 and 1 mm, respectively. 相似文献
7.
This paper determines lower bounds on the number of different cycle lengths in a graph of given minimum degree k and girth g. The most general result gives a lower bound of ckg/8. 相似文献
8.
Erdős has conjectured that every subgraph of the n‐cube Qn having more than (1/2 + o(1))e(Qn) edges will contain a 4‐cycle. In this note we consider ‘layer’ graphs, namely, subgraphs of the cube spanned by the subsets of sizes k − 1, k and k + 1, where we are thinking of the vertices of Qn as being the power set of {1,…, n}. Observe that every 4‐cycle in Qn lies in some layer graph. We investigate the maximum density of 4‐cycle free subgraphs of layer graphs, principally the case k = 2. The questions that arise in this case are equivalent to natural questions in the extremal theory of directed and undirected graphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 66–82, 2000 相似文献
9.
R.H. Schelp 《Discrete Mathematics》2012,312(14):2158-2161
In this paper the following Ramsey–Turán type problem is one of several addressed. For which graphs does there exist a constant such that when is a graph of order the Ramsey number with , then any 2-edge coloring of contains a monochromatic copy of ? Specific results, conjectures, and questions with suggested values for are considered when is an odd cycle, path, or tree of limited maximum degree. Another variant is to 2-edge color a replacement for the graph by a balanced multipartite graph of approximately the same order with the same consequence, a monochromatic . 相似文献
10.
Let G be a graph of order n. We show that if G is a 2-connected graph and max{d(u), d(v)} + |N(u) U N(v)| ≥ n for each pair of vertices u, v at distance two, then either G is hamiltonian or G ?3Kn/3 U T1 U T2, where n ? O (mod 3), and T1 and T2 are the edge sets of two vertex disjoint triangles containing exactly one vertex from each Kn/3. This result generalizes both Fan's and Lindquester's results as well as several others. 相似文献