Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Upper bound involving parameter σ 2 for the rainbow connection number

Upper bound involving parameter σ 2 for the rainbow connection number 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Upper bound involving parameter σ 2 for the rainbow connection number

Loading next page...
 
/lp/springer-journals/upper-bound-involving-parameter-2-for-the-rainbow-connection-number-WgOla9eTKq

References (8)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-013-0247-x
Publisher site
See Article on Publisher Site

Abstract

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).

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 29, 2013

There are no references for this article.