Displaying similar documents to “Lower bounds on van der Waerden numbers: randomized- and deterministic-constructive.”

Spanning trees with many or few colors in edge-colored graphs

Hajo Broersma, Xueliang Li (1997)

Discussiones Mathematicae Graph Theory

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Given a graph G = (V,E) and a (not necessarily proper) edge-coloring of G, we consider the complexity of finding a spanning tree of G with as many different colors as possible, and of finding one with as few different colors as possible. We show that the first problem is equivalent to finding a common independent set of maximum cardinality in two matroids, implying that there is a polynomial algorithm. We use the minimum dominating set problem to show that the second problem is NP-hard. ...

Locally bounded -colorings of trees

C. Bentz, C. Picouleau (2009)

RAIRO - Operations Research

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Given a tree with vertices, we show, by using a dynamic programming approach, that the problem of finding a 3-coloring of respecting local (, associated with prespecified subsets of vertices) color bounds can be solved in log) time. We also show that our algorithm can be adapted to the case of -colorings for fixed .

The color-balanced spanning tree problem

Štefan Berežný, Vladimír Lacko (2005)

Kybernetika

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Suppose a graph G = ( V , E ) whose edges are partitioned into p disjoint categories (colors) is given. In the color-balanced spanning tree problem a spanning tree is looked for that minimizes the variability in the number of edges from different categories. We show that polynomiality of this problem depends on the number p of categories and present some polynomial algorithm.

A few remarks on the history of MST-problem

Jaroslav Nešetřil (1997)

Archivum Mathematicum

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On the background of Borůvka’s pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.