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On a matching distance between rooted phylogenetic trees

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Bogdanowicz D., Giaro K.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 3
669-684
EN
The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs, the values of similarity between clusters are transformed to the final MC-score of the dissimilarity of trees. The analyzed properties give insight into the structure of the metric space generated by MC, its relations with the Matching Split (MS) distance of unrooted trees and asymptotic behavior of the expected distance between binary n-leaf trees selected uniformly in both MC and MS (Θ(n^{3/2})).
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs

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Giaro K., Kubale M.
Discussiones Mathematicae Graph Theory
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2009
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tom 29
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nr 2
361-376
EN
We consider a list cost coloring of vertices and edges in the model of vertex, edge, total and pseudototal coloring of graphs. We use a dynamic programming approach to derive polynomial-time algorithms for solving the above problems for trees. Then we generalize this approach to arbitrary graphs with bounded cyclomatic numbers and to their multicolorings.
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