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71.
Daniel Berend 《Discrete Mathematics》2008,308(20):4670-4695
We find the minimal cutwidth and bisection width values for abelian Cayley graphs with up to 4 generators and present an algorithm for finding the corresponding optimal ordering. We also find minimal cuts of each order. 相似文献
72.
J.A. MacDougall 《Discrete Mathematics》2008,308(13):2756-2763
An edge-magic total labeling on G is a one-to-one map λ from V(G)∪E(G) onto the integers 1,2,…,|V(G)∪E(G)| with the property that, given any edge (x,y), λ(x)+λ(x,y)+λ(y)=k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V(G)|-3 edges. In this paper we study graphs of this maximum size. 相似文献
73.
Philippe Galinier 《Discrete Applied Mathematics》2008,156(2):267-279
Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,…,k}) to each vertex of G so that no edge has both endpoints with the same color. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory. At each iteration, the information contained in the central memory is used for producing an offspring solution which is then possibly improved using a local search algorithm. The so obtained solution is finally used to update the central memory. We describe in this paper an adaptive memory algorithm for the k-coloring problem. Computational experiments give evidence that this new algorithm is competitive with, and simpler and more flexible than, the best known graph coloring algorithms. 相似文献
74.
Manuel Maia 《Discrete Mathematics》2008,308(23):5407-5427
We introduce two new binary operations on combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series in the context of species. It allows us to introduce the notion of multiplicative species, a lifting to the combinatorial level of the classical notion of multiplicative arithmetic function. Interesting combinatorial constructions are introduced; cloned assemblies of structures, hyper-cloned trees, enriched rectangles, etc. Recent research of Cameron, Gewurz and Merola, about the product action in the context of oligomorphic groups, motivated the introduction of the modified arithmetic product. By using the modified arithmetic product we obtain new enumerative results. We also generalize and simplify some results of Canfield, and Pittel, related to the enumerations of tuples of partitions with the restrictions met. 相似文献
75.
We consider the vertex coloring problem, which can be stated as the problem of minimizing the number of labels that can be assigned to the vertices of a graph G such that each vertex receives at least one label and the endpoints of every edge are assigned different labels. In this work, the 0-1 integer programming formulation based on representative vertices is revisited to remove symmetry. The previous polyhedral study related to the original formulation is adapted and generalized. New versions of facets derived from substructures of G are presented, including cliques, odd holes and anti-holes and wheels. In addition, a new class of facets is derived from independent sets of G. Finally, a comparison with the independent sets formulation is provided. 相似文献
76.
Kathryn A. Dowsland 《Discrete Applied Mathematics》2008,156(3):313-324
The focus of this paper is an ant colony optimisation heuristic for the graph colouring problem. We start by showing how a series of improvements enhance the performance of an existing ant colony approach to the problem and then go on to demonstrate that a further strengthening of the construction phase, combined with a tabu search improvement phase, raise the performance to the point where it is able to compete with some of the best-known approaches on a series of benchmark problems. 相似文献
77.
A balanced vertex-coloring of a graph G is a function c from V(G) to {−1,0,1} such that ∑{c(v):v∈V(G)}=0. A subset U of V(G) is called a balanced set if U induces a connected subgraph and ∑{c(v):v∈U}=0. A decomposition V(G)=V1∪?∪Vr is called a balanced decomposition if Vi is a balanced set for 1≤i≤r.In this paper, the balanced decomposition number f(G) of G is introduced; f(G) is the smallest integer s such that for any balanced vertex-coloring c of G, there exists a balanced decomposition V(G)=V1∪?∪Vr with |Vi|≤s for 1≤i≤r. Balanced decomposition numbers of some basic families of graphs such as complete graphs, trees, complete bipartite graphs, cycles, 2-connected graphs are studied. 相似文献
78.
C. M. Da Fonseca 《Annali di Matematica Pura ed Applicata》2008,187(2):251-261
A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues
of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and
used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.
相似文献
79.
《Optimization》2012,61(3):597-624
Some scheduling problems induce a mixed graph coloring, i.e., an assignment of positive integers (colors) to vertices of a mixed graph such that, if two vertices are joined by an edge, then their colors have to be different, and if two vertices are joined by an arc, then the color of the startvertex has to be not greater than the color of the endvertex. We discuss some algorithms for coloring the vertices of a mixed graph with a small number t of colors and present computational results for calculating the chromatic number, i.e., the minimal possible value of such a t . We also study the chromatic polynomial of a mixed graph which may be used for calculating the number of feasible schedules. 相似文献
80.