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91.
Luc G. Chalmet Richard L. Francis Antoon Kolen 《European Journal of Operational Research》1981,6(2):117-124
Given n planar existing facility locations, a planar new facility location X is called efficient if there is no other location Y for which the rectilinear distance between Y and each existing facility is at least as small as between X and each existing facility, and strictly less for at least one existing facility. Rectilinear distances are typically used to measure travel distances between points via rectilinear aisles or street networks. We first present a simple arrow algorithm, based entirely on geometrical analysis, that constructs all efficient locations. We then present a row algorithm which is of order n(log n) that constructs all efficient locations, and establish that no alternative algorithm can be of a lower order. 相似文献
92.
Miroslav Chlebík 《Discrete Applied Mathematics》2006,154(14):1960-1965
In this paper we prove that the PRECOLORING EXTENSION problem on graphs of maximum degree 3 is polynomially solvable, but even its restricted version with 3 colors is NP-complete on planar bipartite graphs of maximum degree 4.The restricted version of LIST COLORING, in which the union of all lists consists of 3 colors, is shown to be NP-complete on planar 3-regular bipartite graphs. 相似文献
93.
The rainbow number for the graph in is defined to be the minimum integer such that any -edge-coloring of contains a rainbow . As one of the most important structures in graphs, the rainbow number of matchings has drawn much attention and has been extensively studied. Jendrol et al. initiated the rainbow number of matchings in planar graphs and they obtained bounds for the rainbow number of the matching in the plane triangulations, where the gap between the lower and upper bounds is . In this paper, we show that the rainbow number of the matching in maximal outerplanar graphs of order is . Using this technique, we show that the rainbow number of the matching in some subfamilies of plane triangulations of order is . The gaps between our lower and upper bounds are only . 相似文献
94.
Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable 总被引:1,自引:0,他引:1
It is known that planar graphs without cycles of length from 4 to 7 are 3-colorable (Borodin et al., 2005) [13] and that planar graphs in which no triangles have common edges with cycles of length from 4 to 9 are 3-colorable (Borodin et al., 2006) [11]. We give a common extension of these results by proving that every planar graph in which no triangles have common edges with k-cycles, where k∈{4,5,7} (or, which is equivalent, with cycles of length 3, 5 and 7), is 3-colorable. 相似文献
95.
We illustrate a new way to study the stability problem in celestial mechanics. In this paper, using the variational nature of elliptic Lagrangian solutions in the planar three-body problem, we study the relation between Morse index and its stability via Maslov-type index theory of periodic solutions of Hamiltonian system. For elliptic Lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the Morse index, which is the key to understand the stability problem. As a special case, we provide a criterion to spectral stability of relative equilibrium. 相似文献
96.
This paper considers the problem of locating a single facility in the presence of a line barrier that occurs randomly on a given horizontal route on the plane. The objective is to locate this new facility such that the sum of the expected rectilinear distances from the facility to the demand points in the presence of the probabilistic barrier is minimized. Some properties of the problem are reported, a solution algorithm is provided with an example problem, and some future extensions to the problem are discussed. 相似文献
97.
An induced matching in a graph G=(V,E) is a matching M such that (V,M) is an induced subgraph of G. Clearly, among two vertices with the same neighbourhood (called twins) at most one is matched in any induced matching, and if one of them is matched then there is another matching of the same size that matches the other vertex. Motivated by this, Kanj et al. [10] studied induced matchings in twinless graphs. They showed that any twinless planar graph contains an induced matching of size at least and that there are twinless planar graphs that do not contain an induced matching of size greater than . We improve both these bounds to , which is tight up to an additive constant. This implies that the problem of deciding whether a planar graph has an induced matching of size k has a kernel of size at most 28k. We also show for the first time that this problem is fixed parameter tractable for graphs of bounded arboricity.Kanj et al. also presented an algorithm which decides in -time whether an n-vertex planar graph contains an induced matching of size k. Our results improve the time complexity analysis of their algorithm. However, we also show a more efficient -time algorithm. Its main ingredient is a new, O∗(4l)-time algorithm for finding a maximum induced matching in a graph of branch width at most l. 相似文献
98.
The class of planar graphs has unbounded treewidth, since the k×k grid, ∀k∈N, is planar and has treewidth k. So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49. 相似文献
99.
Toshiki Endo 《Topology and its Applications》2010,157(6):1002-1010
We say that a link L1 is an s-major of a link L2 if any diagram of L1 can be transformed into a diagram of L2 by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knots and links with the crossing number less than or equal to six. The proofs are given by graph-theoretic methods. 相似文献
100.