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41.
Pawel Winter 《Operations Research Letters》2005,33(4):395-402
We give a number of structural results for the problem of constructing a minimum-length 2-connected network for a set of terminals in a graph, where edge-weights satisfy the triangle inequality. A new algorithmic framework, based on our structural results, is given. 相似文献
42.
43.
Yuichiro Fujiwara 《Discrete Mathematics》2007,307(13):1551-1558
A Steiner 2-design S(2,k,v) is said to be halvable if the block set can be partitioned into two isomorphic sets. This is equivalent to an edge-disjoint decomposition of a self-complementary graph G on v vertices into Kks. The obvious necessary condition of those orders v for which there exists a halvable S(2,k,v) is that v admits the existence of an S(2,k,v) with an even number of blocks. In this paper, we give an asymptotic solution for various block sizes. We prove that for any k?5 or any Mersenne prime k, there is a constant number v0 such that if v>v0 and v satisfies the above necessary condition, then there exists a halvable S(2,k,v). We also show that a halvable S(2,2n,v) exists for over a half of possible orders. Some recursive constructions generating infinitely many new halvable Steiner 2-designs are also presented. 相似文献
44.
It is well known that there is a planar sloop of cardinality n for each n≡2 or 4 (mod 6) (Math. Z. 111 (1969) 289–300). A semi-planar sloop is a simple sloop in which each triangle either generates the whole sloop or the 8-element sloop. In fact, Quackenbush (Canad. J. Math. 28 (1976) 1187–1198) has stated that there should be such semi-planar sloops. In this paper, we construct a semi-planar sloop of cardinality 2n for each n≡2 or 4 (mod 6). Consequently, we may say that there is a semi-planar sloop that is not planar of cardinality m for each m>16 and m≡4 or 8 (mod 12). Moreover, Quackenbush (Canad. J. Math. 28 (1976) 1187–1198) has proved that each finite simple planar sloop generates a variety, which covers the smallest non-trivial subvariety (the variety of all Boolean sloops) of the lattice of the subvarieties of all sloops. Similarly, it is easy to show that each finite semi-planar sloop generates another variety, which also covers the variety of all Boolean sloops. Furthermore, for any finite simple sloop
of cardinality n, the author (Beiträge Algebra Geom. 43 (2) (2002) 325–331) has constructed a subdirectly irreducible sloop
of cardinality 2n and containing
as the only proper normal subsloop. Accordingly, if
is a semi-planar sloop, then the variety
generated by
properly contains the subvariety
. 相似文献
45.
In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some
switchbox routing problems of VLSI-design and report on our computational experience. This includes a brief discussion of
separation algorithms, a new LP-based primal heuristic and implementation details. The paper is based on the polyhedral theory
for the Steiner tree packing polyhedron developed in our companion paper (this issue) and meant to turn this theory into an
algorithmic tool for the solution of practical problems. 相似文献
46.
Roger W. Barnard Clint Richardson Alexander Yu. Solynin 《Proceedings of the American Mathematical Society》2005,133(7):2091-2099
For the standard class of normalized univalent functions analytic in the unit disk , we consider a problem on the minimal area of the image concentrated in any given half-plane. This question is related to a well-known problem posed by A. W. Goodman in 1949 that regards minimizing area covered by analytic univalent functions under certain geometric constraints. An interesting aspect of this problem is the unexpected behavior of the candidates for extremal functions constructed via geometric considerations.
47.
Peter Danziger Peter Dukes Terry Griggs Eric Mendelsohn 《Graphs and Combinatorics》2006,22(3):311-329
A Steiner triple system of order v, or STS(v), is a pair (V, ) with V a set of v points and a set of 3-subsets of V called blocks or triples, such that every pair of distinct elements of V occurs in exactly one triple. The intersection problem for STS is to determine the possible numbers of blocks common to two Steiner triple systems STS(u), (U, ), and STS(v), (V, ), with U⊆V. The case where U=V was solved by Lindner and Rosa in 1975. Here, we let U⊂V and completely solve this question for v−u=2,4 and for v≥2u−3.
supported by NSERC research grant #OGP0170220.
supported by NSERC postdoctoral fellowship.
supported by NSERC research grant #OGP007621. 相似文献
48.
Let be a set of at least two vertices in a graph . A subtree of is a -Steiner tree if . Two -Steiner trees and are edge-disjoint (resp. internally vertex-disjoint) if (resp. and ). Let (resp. ) be the maximum number of edge-disjoint (resp. internally vertex-disjoint) -Steiner trees in , and let (resp. ) be the minimum (resp. ) for ranges over all -subset of . Kriesell conjectured that if for any , then . He proved that the conjecture holds for . In this paper, we give a short proof of Kriesell’s Conjecture for , and also show that (resp. ) if (resp. ) in , where . Moreover, we also study the relation between and , where is the line graph of . 相似文献
49.
《组合设计杂志》2018,26(1):5-11
We call a partial Steiner triple system C (configuration) t‐Ramsey if for large enough n (in terms of ), in every t‐coloring of the blocks of any Steiner triple system STS(n) there is a monochromatic copy of C. We prove that configuration C is t‐Ramsey for every t in three cases:
- C is acyclic
- every block of C has a point of degree one
- C has a triangle with blocks 123, 345, 561 with some further blocks attached at points 1 and 4
50.
关于Steiner问题的一个注记——连接五点之最小网络的一种寻优方案 总被引:2,自引:0,他引:2
本文讨论如何寻找连接平面上五个给定点的最小网络这一问题.通过发展越民义证明Pollack在1978年所给出的一个关于寻找连接平面上四个给定点的最小网络的重要结论的方法,我们给出了一个采用简单几何作图方法快速求解该问题的方案. 相似文献