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911.
Given a graph G=(V,E), the Hamiltonian completion number of G, HCN(G), is the minimum number of edges to be added to G to make it Hamiltonian. This problem is known to be
-hard even when G is a line graph. In this paper, local search algorithms for finding HCN(G) when G is a line graph are proposed. The adopted approach is mainly based on finding a set of edge-disjoint trails that dominates
all the edges of the root graph of G. Extensive computational experiments conducted on a wide set of instances allow to point out the behavior of the proposed
algorithms with respect to both the quality of the solutions and the computation time. 相似文献
912.
Suppose G=(V, E) is a graph and p ≥ 2q are positive integers. A (p, q)‐coloring of G is a mapping ?: V → {0, 1, …, p‐1} such that for any edge xy of G, q ≤ |?(x)‐?(y)| ≤ p‐q. A color‐list is a mapping L: V → ({0, 1, …, p‐1}) which assigns to each vertex v a set L(v) of permissible colors. An L‐(p, q)‐coloring of G is a (p, q)‐coloring ? of G such that for each vertex v, ?(v) ∈ L(v). We say G is L‐(p, q)‐colorable if there exists an L‐(p, q)‐coloring of G. A color‐size‐list is a mapping ? which assigns to each vertex v a non‐negative integer ?(v). We say G is ?‐(p, q)‐colorable if for every color‐list L with |L(v)| = ?(v), G is L‐(p, q)‐colorable. In this article, we consider list circular coloring of trees and cycles. For any tree T and for any p ≥ 2q, we present a necessary and sufficient condition for T to be ?‐(p, q)‐colorable. For each cycle C and for each positive integer k, we present a condition on ? which is sufficient for C to be ?‐(2k+1, k)‐colorable, and the condition is sharp. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 249–265, 2007 相似文献
913.
914.
We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network
localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories
to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore,
we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient
criterion for checking whether a given instance of the localization problem has a unique realization in
using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will
identify all strongly localizable sub-networks in the input network.
A preliminary version of this paper has appeared in the Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2005. 相似文献
915.
Edith Hemaspaandra Lane A. Hemaspaandra Stanis?aw P. Radziszowski 《Discrete Applied Mathematics》2007,155(2):103-118
We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c?1 of deletion:
- (1)
- , , , and .
- (2)
- For all k?2, and .
- (3)
- For all k?2, .
- (4)
- .
- (5)
- For all k?2, .
916.
The likelihood approach is common in linkage analysis of large extended pedigrees. Various peeling procedures, based on the conditional independence of separate parts of a pedigree, are typically used for likelihood calculations. A peeling order may significantly affect the complexity of such calculations, particularly for pedigrees with loops or when many pedigrees members have unknown genotypes. Several algorithms have been proposed to address this problem for pedigrees with loops. However, the problem has not been solved for pedigrees without loops until now. In this paper, we suggest a new graph theoretic algorithm for optimal selection of peeling order in zero-loop pedigrees with incomplete genotypic information. It is especially useful when multiple likelihood calculation is needed, for example, when genetic parameters are estimated or linkage with multiple marker loci is tested. The algorithm can be easily introduced into the existing software packages for linkage analysis based on the Elston-Stewart algorithm for likelihood calculation. The algorithm was implemented in a software package PedPeel, which is freely available at http://mga.bionet.nsc.ru/nlru/. 相似文献
917.
Given a simple connected graph G = (V, E) the geodetic closure of a subset S of V is the union of all sets of nodes lying on some geodesic (or shortest path) joining a pair of nodes . The geodetic number, denoted by g(G), is the smallest cardinality of a node set S
* such that I[S
*] = V. In “The geodetic number of a graph”, [Harary et al. in Math. Comput. Model. 17:89–95, 1993] propose an incorrect algorithm to find the geodetic number of a graph G. We provide counterexamples and show why the proposed approach must fail. We then develop a 0–1 integer programming model
to find the geodetic number. Computational results are given. 相似文献
918.
919.
920.
A graph H is called a supersubdivison of a graph G if H is obtained from G by replacing every edge uv of G by a complete bipartite graph K2,m (m may vary for each edge) by identifying u and v with the two vertices in K2,m that form one of the two partite sets. We denote the set of all such supersubdivision graphs by SS(G). Then, we prove the following results.
- 1. Each non-trivial connected graph G and each supersubdivision graph HSS(G) admits an α-valuation. Consequently, due to the results of Rosa (in: Theory of Graphs, International Symposium, Rome, July 1966, Gordon and Breach, New York, Dunod, Paris, 1967, p. 349) and El-Zanati and Vanden Eynden (J. Combin. Designs 4 (1996) 51), it follows that complete graphs K2cq+1 and complete bipartite graphs Kmq,nq can be decomposed into edge disjoined copies of HSS(G), for all positive integers m,n and c, where q=|E(H)|.
- 2. Each connected graph G and each supersubdivision graph in SS(G) is strongly n-elegant, where n=|V(G)| and felicitous.
- 3. Each supersubdivision graph in EASS(G), the set of all even arbitrary supersubdivision graphs of any graph G, is cordial.