Showing papers on "Spanning tree published in 1971"
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.
Abstract: The relationship between the symmetric traveling-salesman problem and the minimum spanning tree problem yields a sharp lower bound on the cost of an optimum tour. An efficient iterative method for approximating this bound closely from below is presented. A branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it, ranging in size up to sixty-four cities. The bounds used are so sharp that the search trees are minuscule compared to those normally encountered in combinatorial problems of this type.
1,041 citations
TL;DR: In this article, it is shown how the ideas of Edmonds [1], Gustin [2], and Youngs [3] can be used to formulate precisely the generalization of this result to graphs imbedded in any orientable surface.
30 citations
TL;DR: In this paper, the family of minimum forest covers of varying cardinality is shown to be related to the minimum spanning tree of the graph, and a method is discussed for obtaining minimum covers of specified cardinality.
Abstract: Given a weighted graph, a method is discussed for obtaining minimum covers of specified cardinality. It is shown that the family of minimum forest covers of varying cardinality is related to the minimum spanning tree of the graph.
16 citations
01 Jan 1971
4 citations
2 citations
Abstract: The problem of counting spanning trees in linear graphs is dealt with. A quite general indirect approach, based on the analysis of the complementary graph, is followed and a new counting formula, which applies to any kind of linear non-oriented graph, is given. The paper ends with some comments and concluding remarks.
1 citations