Results 41 to 50 of about 101,543 (166)
Rainbow Connectivity of Cacti and of Some Infinite Digraphs
Discussiones Mathematicae Graph Theory, 2017 An arc-coloured digraph D = (V,A) is said to be rainbow connected if for every pair {u, v} ⊆ V there is a directed uv-path all whose arcs have different colours and a directed vu-path all whose arcs have different colours.
Alva-Samos Jesús +1 more
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Oriented diameter and rainbow connection number of a graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Xiaolong Huang +3 more
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The rainbow connection number of 2-connected graphs
Discrete Mathematics, 2013 The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most the ceiling of ...
Ekstein, Jan +6 more
openaire +2 more sources
BarekengThe rainbow connection was first introduced by Chartrand in 2006 and then in 2009 Krivelevich and Yuster first time introduced the rainbow vertex connection. Let graph be a connected graph.
Muhammad Ilham Nurfaizi Annadhifi +3 more
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Rainbow Connection of Random Regular Graphs [PDF]
, 2014 An edge colored graph $G$ is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors that are needed in ...
Dudek, Andrzej +2 more
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Note on Rainbow Connection in Oriented Graphs with Diameter 2
Theory and Applications of Graphs, 2014 In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter $2$. For a tournament $T$ of diameter $2$, we show $2 \leq \overrightarrow{rc}(T) \leq 3$.
Rebecca Holliday +2 more
doaj +1 more source
The Strong 3-Rainbow Index of Graphs Containing Three Cycles
InPrime, 2023 The concept of a strong k-rainbow index is a generalization of a strong rainbow connection number, which has an interesting application in security systems in a communication network.
Zata Yumni Awanis
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Rainbow connection in $3$-connected graphs [PDF]
, 2010 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 by $rc(G)$, is the smallest number of colors that are needed in ...
Li, Xueliang, Shi, Yongtang
core
The strong rainbow vertex-connection of graphs [PDF]
, 2012 A vertex-colored graph $G$ is said to be rainbow vertex-connected if every two vertices of $G$ are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected
Li, Xueliang, Mao, Yaping, Shi, Yongtang
core
On (strong) proper vertex-connection of graphs
, 2015 A path in a vertex-colored graph is a {\it vertex-proper path} if any two internal adjacent vertices differ in color. A vertex-colored graph is {\it proper vertex $k$-connected} if any two vertices of the graph are connected by $k$ disjoint vertex-proper
Jiang, Hui +3 more
core +1 more source