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Partitioning complete graphs by heterochromatic trees

Partitioning complete graphs by heterochromatic trees A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by t r (G), is the minimum positive integer p such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we determine the heterochromatic tree partition number of r-edge-colored complete graphs. We also find at most t r (K n ) vertex-disjoint heterochromatic trees to cover all the vertices in polynomial time for a given r-edge-coloring of K n . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Partitioning complete graphs by heterochromatic trees

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0177-z
Publisher site
See Article on Publisher Site

Abstract

A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by t r (G), is the minimum positive integer p such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we determine the heterochromatic tree partition number of r-edge-colored complete graphs. We also find at most t r (K n ) vertex-disjoint heterochromatic trees to cover all the vertices in polynomial time for a given r-edge-coloring of K n .

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 21, 2012

References