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Sourav Chakraborty, E. Fischer, A. Matsliah, R. Yuster (2009)
Hardness and Algorithms for Rainbow Connectivity
Y. Caro, A. Lev, Y. Roditty, Z. Tuza, R. Yuster (2008)
On Rainbow ConnectionElectron. J. Comb., 15
X Li, Y Sun (2012)
Rainbow Connections of Graphs, Springer Briefs in Mathematics
G. Chartrand, Garry Johns, K. McKeon, Ping Zhang (2008)
Rainbow connection in graphs, 133
JA Bondy (2008)
Murty U.S.R. Graph Theory
Xueliang Li, Yuefang Sun (2012)
Rainbow Connections of Graphs
Xueliang Li, Yongtang Shi, Yuefang Sun (2011)
Rainbow Connections of Graphs: A SurveyGraphs and Combinatorics, 29
L. Chandran, Anita Das, D. Rajendraprasad, Nithin Varma (2010)
Rainbow connection number and connected dominating setsJournal of Graph Theory, 71
Let G be a connected graph of order n. The rainbow connection number rc(G) of G was introduced by Chartrand et al. Chandran et al. used the minimum degree δ of G and obtained an upper bound that rc(G) ≤ 3n/(δ +1)+3, which is tight up to additive factors. In this paper, we use the minimum degree-sum σ 2 of G to obtain a better bound $$rc(G) \leqslant \tfrac{{6n}} {{\sigma _2 + 2}} + 8$$ , especially when δ is small (constant) but σ 2 is large (linear in n).
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Nov 29, 2013
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