# 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

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topArnfried 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 -

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