Rainbow connections of graphs: A survey

X Li, Y Shi, Y Sun - Graphs and combinatorics, 2013 - Springer
The concept of rainbow connection was introduced by Chartrand et al.[14] in 2008. It is
interesting and recently quite a lot papers have been published about it. In this survey we …

[HTML][HTML] A survey of Nordhaus–Gaddum type relations

M Aouchiche, P Hansen - Discrete Applied Mathematics, 2013 - Elsevier
In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product
of the chromatic number of a graph and its complement, in terms of the order of the graph …

[HTML][HTML] Proper connection of graphs

V Borozan, S Fujita, A Gerek, C Magnant… - Discrete …, 2012 - Elsevier
An edge-colored graph G is k-proper connected if every pair of vertices is connected by k
internally pairwise vertex-disjoint proper colored paths. The k-proper connection number of …

An updated survey on rainbow connections of graphs-a dynamic survey

X Li, Y Sun - Theory and Applications of Graphs, 2017 - digitalcommons.georgiasouthern …
The concept of rainbow connection was introduced by Chartrand, Johns, McKeon and
Zhang in 2008. Nowadays it has become a new and active subject in graph theory. There is …

Rainbow connection number and connected dominating sets

L Sunil Chandran, A Das… - Journal of Graph …, 2012 - Wiley Online Library
The rainbow connection number of a connected graph is the minimum number of colors
needed to color its edges, so that every pair of its vertices is connected by at least one path …

On rainbow antimagic coloring of special graphs

BJ Septory, MI Utoyo, B Sulistiyono… - Journal of Physics …, 2021 - iopscience.iop.org
Abstract Let G (V, E) be a connected, undirected and simple graph with vertex set V (G) and
edge set E (G). A labeling of a graph G is a bijection f from V (G) to the set {1, 2,...,| V (G)|} …

The rainbow (vertex) connection number of pencil graphs

DNS Simamora, ANM Salman - Procedia Computer Science, 2015 - Elsevier
An edge colored graph G=(V (G), E (G)) is said rainbow connected, if any two vertices are
connnected by a path whose edges have distinct colors. The rainbow connection number of …

On the rainbow vertex-connection

X Li, Y Shi - arxiv preprint arxiv:1012.3504, 2010 - arxiv.org
A vertex-colored graph is {\it rainbow vertex-connected} if any two vertices are connected by
a path whose internal vertices have distinct colors, which was introduced by Krivelevich and …

The complexity of determining the rainbow vertex-connection of a graph

L Chen, X Li, Y Shi - Theoretical Computer Science, 2011 - Elsevier
A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a
path whose internal vertices have distinct colors, which was introduced by Krivelevich and …

Rainbow connection in graphs with minimum degree three

I Schiermeyer - International Workshop on Combinatorial Algorithms, 2009 - Springer
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path
whose edges have distinct colours. The rainbow connection number of a connected graph …