More on complementary trees
TLDR
It is shown that a graph with no multiple edges on n vertices, n >= 5, with 2(n-2) arcs labelled 1,..., n-1 and 1',...,n-1' having at least one spanning tree whose arcs include no pair (j,[email protected]?), has at least six of them.About:
This article is published in Discrete Mathematics.The article was published on 1976-01-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Spanning tree & Path graph.read more
Citations
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Kleitman and combinatorics: a celebration
TL;DR: A discussion of the history, the mathematics, and the charm of Daniel J. Kleitman.
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A note on properties for a complementary graph and its tree graph
Abulimiti Yiming,Masami Yasuda +1 more
TL;DR: In this paper, a complementary (tree) graph in n-th (n ≥ 2) order is defined and discussed its property, and a relation to the complete graph K 2n and also to the tree graph associated with the complementary graph is studied.
References
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Some Abstract Pivot Algorithms
Curtis Greene,Thomas L. Magnanti +1 more
TL;DR: Several problems in the theory of combinatorial geometries (or matroids) are solved by means of algorithms which involve the notion of abstract pivots, such as the Edmonds-Fulkerson partition theorem, which is applied to prove a number of generalized exchange properties for bases as mentioned in this paper.
ReportDOI
Complementary spanning trees
TL;DR: In this article, the authors considered the problem of constructing a spanning tree such that no two of its arcs belong to the same club and provided necessary and sufficient conditions for such trees to exist.
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Complementary bases of a matroid
TL;DR: It is proved that there exist at least 2^m bases, called complementary bases, of M with the property that only one of each complementary pair e"j, e'"j is contained in any base.