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Rainbow connections of bioriented graphs. [PDF]
Heliyon, 2023 For a directed graph D, it's deemed rainbow connected if each arc is assigned a different color, so that all paths from the vertex u to the vertex v are rainbow connected. Rainbow connection number refers to how many colors are needed in D to achieve rainbow connectivity.
Wang L, Liu S, Jiang H.
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Strong rainbow connection in digraphs
Discrete Applied Mathematics, 2018 International audienceAn arc-coloured digraph is strongly rainbow connected if for every pair of vertices (u, v) there exists a shortest path from u to v all of whose arcs have different colours.
Elżbieta Sidorowicz, Eric Sopena
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Proper Rainbow Connection Number of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-coloured graph is called a rainbow path if its edges receive pairwise distinct colours. An edge-coloured graph is said to be rainbow connected if any two distinct vertices of the graph are connected by a rainbow path.
Schiermeyer Ingo, Doan Trung Duy
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Rainbow Connection In Sparse Graphs
Discussiones Mathematicae Graph Theory, 2013 An edge-coloured connected graph $G = (V,E)$ is called rainbow-connected if each pair of distinct vertices of $G$ is connected by a path whose edges have distinct colours.
Kemnitz, Arnfried +3 more
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Rainbow connection in graphs [PDF]
Mathematica Bohemica, 2008 summary:Let $G$ be a nontrivial connected graph on which is defined a coloring $c\: E(G) \rightarrow \lbrace 1, 2, \ldots , k\rbrace $, $k \in {\mathbb{N}}$, of the edges of $G$, where adjacent edges may be colored the same.
Johns, Garry L. +3 more
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Rainbow Connection in 3-Connected Graphs [PDF]
Graphs and Combinatorics, 2012 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 order to make $G$ rainbow connected.
Xueliang Li +2 more
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Rainbow vertex connection of digraphs [PDF]
Journal of Combinatorial Optimization, 2017 22 pages, 3 ...
Yongtang Shi, Shi Yongtang
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Rainbow Connection of Random Regular Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2018 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 order to ...
Alan Frieze (3880564) +2 more
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Rainbow connection in oriented graphs
Discrete Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Dorbec +2 more
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Total rainbow connection of digraphs
Discrete Applied Mathematics, 2018 An edge-coloured path is rainbow if its edges have distinct colours. For a connected graph $G$, the rainbow connection number (resp. strong rainbow connection number) of $G$ is the minimum number of colours required to colour the edges of $G$ so that, any two vertices of $G$ are connected by a rainbow path (resp. rainbow geodesic).
Colton Magnant, Yongtang Shi
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