Rainbow Connection Number of Dense Graphs

• Autorzy: Xueliang Li , Mengmeng Liu , Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

edge-colored graph; rainbow coloring; rainbow connection number

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 3
• Strony: 603-611

Daty

wydano

2013-07-01

online

2013-07-30

Twórcy

autor

Xueliang Li

• Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, China

autor

Mengmeng Liu

• Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, China

autor

Ingo Schiermeyer

• Institut für Diskrete Mathematik und Algebra echnische Universität Bergakademie Freiberg 09596 Freiberg, Germany

Bibliografia

• [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.
• [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]

Identyfikatory

DOI

10.7151/dmgt.1692