# Rainbow Connection Number of Dense Graphs

Xueliang Li; Mengmeng Liu; Ingo Schiermeyer

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 3, page 603-611
- ISSN: 2083-5892

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topXueliang Li, Mengmeng Liu, and Ingo Schiermeyer. "Rainbow Connection Number of Dense Graphs." Discussiones Mathematicae Graph Theory 33.3 (2013): 603-611. <http://eudml.org/doc/267532>.

@article{XueliangLi2013,

abstract = {An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we show that rc(G) ≤ 3 if |E(G)| ≥ [...] + 2, and rc(G) ≤ 4 if |E(G)| ≥ [...] + 3. These bounds are sharp.},

author = {Xueliang Li, Mengmeng Liu, Ingo Schiermeyer},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {edge-colored graph; rainbow coloring; rainbow connection number},

language = {eng},

number = {3},

pages = {603-611},

title = {Rainbow Connection Number of Dense Graphs},

url = {http://eudml.org/doc/267532},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Xueliang Li

AU - Mengmeng Liu

AU - Ingo Schiermeyer

TI - Rainbow Connection Number of Dense Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 3

SP - 603

EP - 611

AB - An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we show that rc(G) ≤ 3 if |E(G)| ≥ [...] + 2, and rc(G) ≤ 4 if |E(G)| ≥ [...] + 3. These bounds are sharp.

LA - eng

KW - edge-colored graph; rainbow coloring; rainbow connection number

UR - http://eudml.org/doc/267532

ER -

## References

top- [1] J.A. Bondy and U.S.R. Murty, Graph Theory (GTM 244, Springer, 2008).
- [2] G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang, Rainbow connection in graphs, Math. Bohem. 133 (2008) 85-98. Zbl1199.05106
- [3] A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24-28.
- [4] A. Kemnitz and I. Schiermeyer, Graphs with rainbow connection number two, Disscuss. Math. Graph Theory 31 (2011) 313-320. doi:10.7151/dmgt.1547[Crossref]
- [5] X. Li and Y. Sun, Rainbow Connections of Graphs (SpringerBriefs in Math., Springer, New York, 2012). doi:10.1007/978-1-4614-3119-0 [Crossref]

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