Rainbow connection number, bridges and radius
Jiuying Dong, Xueliang Li

TL;DR
This paper investigates the rainbow connection number of connected graphs, providing bounds based on radius and bridges, and generalizes previous results by Basavaraju et al. with new structural insights.
Contribution
The paper introduces a method to bound the rainbow connection number using connected dominating sets and bridges, extending prior bounds to more general graph classes.
Findings
Bound on $rc(G)$ in terms of radius and bridges.
Construction of connected dominating sets with controlled rainbow connection.
Generalization of Basavaraju et al.'s result to broader graph classes.
Abstract
Let be a connected graph. The notion \emph{the rainbow connection number } of a graph was introduced recently by Chartrand et al. Basavaraju et al. showed that for every bridgeless graph with radius , , and the bound is tight. In this paper, we prove that if is a connected graph, and is a connected -step dominating set of , then has a connected -step dominating set such that , where is the number of bridges in . Furthermore, for a connected graph with radius , let be the center of , and . Then has connected dominating sets satisfying , and ,…
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph theory and applications
