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91.
Ryo Hanaki 《Journal of Graph Theory》2012,70(1):67-79
We present four new classes of graphs, two of which every member has a strongly almost trivial embedding, and the other two of which every member has no strongly almost trivial embeddings. We show that the property that a graph has a strongly almost trivial embedding and the property that a graph has no strongly almost trivial embeddings are not inherited by minors. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 相似文献
92.
Tomáš Kulich 《Random Structures and Algorithms》2012,41(2):282-291
In this paper we present an estimation for the diameter of random subgraph of a hypercube. In the article by A. V. Kostochka (Random Struct Algorithms 4 (1993) 215–229) the authors obtained lower and upper bound for the diameter. According to their work, the inequalities n + mp ≤ D(Gn) ≤ n + mp + 8 almost surely hold as n → ∞, where n is dimension of the hypercube and mp depends only on sampling probabilities. It is not clear from their work, whether the values of the diameter are really distributed on these 9 values, or whether the inequality can be sharpened. In this paper we introduce several new ideas, using which we are able to obtain an exact result: D(Gn) = n + mp (almost surely). © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 相似文献
93.
The point‐line geometry known as a partial quadrangle (introduced by Cameron in 1975) has the property that for every point/line non‐incident pair (P, ?), there is at most one line through P concurrent with ?. So in particular, the well‐studied objects known as generalized quadrangles are each partial quadrangles. An intriguing set of a generalized quadrangle is a set of points which induces an equitable partition of size two of the underlying strongly regular graph. We extend the theory of intriguing sets of generalized quadrangles by Bamberg, Law and Penttila to partial quadrangles, which gives insight into the structure of hemisystems and other intriguing sets of generalized quadrangles. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:217‐245, 2011 相似文献
94.
Kinkar Ch. Das 《Applied mathematics and computation》2011,217(18):7420-7426
We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained. 相似文献
95.
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98.
For a positive integer n, does there exist a vertex-transitive graph Γ on n vertices which is not a Cayley graph, or, equivalently, a graph Γ on n vertices such that Aut Γ is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, Marusic and Scapellato, and McKay and the second author) has produced answers to this question if n is prime, or divisible by the square of some prime, or if n is the product of two distinct primes. In this paper we consider the simplest unresolved case for even integers, namely for integers of the form n = 2pq, where 2 < q < p, and p and q are primes. We give a new construction of an infinite family of vertex-transitive graphs on 2pq vertices which are not Cayley graphs in the case where p ≡ 1 (mod q). Further, if p ? 1 (mod q), p ≡ q ≡ 3(mod 4), and if every vertex-transitive graph of order pq is a Cayley graph, then it is shown that, either 2pq = 66, or every vertex-transitive graph of order 2pq admitting a transitive imprimitive group of automorphisms is a Cayley graph. 相似文献
99.
关于Abel群上Cayley图的Hamilton圈分解 总被引:3,自引:0,他引:3
设G(F,T∩T^-1)是有限Abel群F上的Cayley图,T∩T^-1只含2阶元,此文证明了当T是F的极小生成元集时,若d(G)=2k,则G是k个边不相交的Hamilton圈的并,若d(G)=2k+1,则G是k个边不相交的Hamilton圈与一个1-因子的并。 相似文献
100.
We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance. 相似文献