Rainbow Connection In Sparse Graphs

Arnfried Kemnitz; Jakub Przybyło; Ingo Schiermeyer; Mariusz Woźniak

Discussiones Mathematicae Graph Theory (2013)

  • Volume: 33, Issue: 1, page 181-192
  • ISSN: 2083-5892

Abstract

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An edge-coloured connected graph G = (V,E) is called rainbow-connected if each pair of distinct vertices of G is connected by a path whose edges have distinct colours. The rainbow connection number of G, denoted by rc(G), is the minimum number of colours such that G is rainbow-connected. In this paper we prove that rc(G) ≤ k if |V (G)| = n and for all integers n and k with n − 6 ≤ k ≤ n − 3. We also show that this bound is tight.

How to cite

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Arnfried Kemnitz, et al. "Rainbow Connection In Sparse Graphs." Discussiones Mathematicae Graph Theory 33.1 (2013): 181-192. <http://eudml.org/doc/267722>.

@article{ArnfriedKemnitz2013,
abstract = {An edge-coloured connected graph G = (V,E) is called rainbow-connected if each pair of distinct vertices of G is connected by a path whose edges have distinct colours. The rainbow connection number of G, denoted by rc(G), is the minimum number of colours such that G is rainbow-connected. In this paper we prove that rc(G) ≤ k if |V (G)| = n and for all integers n and k with n − 6 ≤ k ≤ n − 3. We also show that this bound is tight.},
author = {Arnfried Kemnitz, Jakub Przybyło, Ingo Schiermeyer, Mariusz Woźniak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {rainbow-connected graph; rainbow colouring; rainbow connection number},
language = {eng},
number = {1},
pages = {181-192},
title = {Rainbow Connection In Sparse Graphs},
url = {http://eudml.org/doc/267722},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Arnfried Kemnitz
AU - Jakub Przybyło
AU - Ingo Schiermeyer
AU - Mariusz Woźniak
TI - Rainbow Connection In Sparse Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 1
SP - 181
EP - 192
AB - An edge-coloured connected graph G = (V,E) is called rainbow-connected if each pair of distinct vertices of G is connected by a path whose edges have distinct colours. The rainbow connection number of G, denoted by rc(G), is the minimum number of colours such that G is rainbow-connected. In this paper we prove that rc(G) ≤ k if |V (G)| = n and for all integers n and k with n − 6 ≤ k ≤ n − 3. We also show that this bound is tight.
LA - eng
KW - rainbow-connected graph; rainbow colouring; rainbow connection number
UR - http://eudml.org/doc/267722
ER -

References

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