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An updated survey on rainbow connections of graphs - a dynamic survey
Theory and Applications of Graphs, 2017 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 a book on this topic by Li and Sun in 2012, and a survey paper by Li, Shi and Sun in
Xueliang Li, Yuefang Sun
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BATAS ATAS RAINBOW CONNECTION NUMBER PADA GRAF BUCKMINSTERFULLERENE
Jurnal Matematika UNAND, 2022 Misalkan G adalah suatu graf terhubung tak trivial. Suatu pewarnaan c : E(G) → {1, 2, ..., k}, k ∈ N pada graf G adalah suatu pewarnaan sisi di G sedemikian sehingga setiap sisi bertetangga boleh berwarna sama.
Fitri - Anggalia +2 more
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Hardness and Algorithms for Rainbow Connectivity [PDF]
, 2009 An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G
Chakraborty, Sourav +3 more
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Rainbow Matchings in Properly-Colored Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2019 A hypergraph $H$ is properly colored if for every vertex $v\in V(H)$, all the edges incident to $v$ have distinct colors. In this paper, we show that if $H_{1}, \ldots, H_{s}$ are properly-colored $k$-uniform hypergraphs on $n$ vertices, where $n\geq3k^{2}s$, and $e(H_{i})>{{n}\choose {k}}-{{n-s+1}\choose {k}}$, then there exists a rainbow matching
Huang, Hao, Li, Tong, Wang, Guanghui
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Barekeng, 2022 If be a graph and edge coloring of G is a function , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special
Sumarno Ismail +3 more
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Coloring the Cube with Rainbow Cycles [PDF]
The Electronic Journal of Combinatorics, 2013 For every even positive integer $k\ge 4$ let $f(n,k)$ denote the minimim number of colors required to color the edges of the $n$-dimensional cube $Q_n$, so that the edges of every copy of the $k$-cycle $C_k$ receive $k$ distinct colors. Faudree, Gyárfás, Lesniak and Schelp proved that $f(n,4)=n$ for $n=4$ or $n>5$.
Mubayi, Dhruv, Stading, Randall
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Distance-Local Rainbow Connection Number
Discussiones Mathematicae Graph Theory, 2022 Under an edge coloring (not necessarily proper), a rainbow path is a path whose edge colors are all distinct. The d-local rainbow connection number lrcd(G) (respectively, d-local strong rainbow connection number lsrcd(G)) is the smallest number of colors
Septyanto Fendy, Sugeng Kiki A.
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Rainbow Matching in Edge-Colored Graphs [PDF]
The Electronic Journal of Combinatorics, 2010 A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex $v$ is the number of different colors on edges incident to $v$. Wang and Li conjectured that for $k\geq 4$, every edge-colored graph with minimum color degree at least $k$ contains a rainbow matching of size at least $\left\lceil k/
LeSaulnier, Timothy D. +3 more
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Rainbow Connection on Amal(Fn,xz,m) Graphs and Amal(On,xz,m) Graphs
Contemporary Mathematics and Applications (ConMathA)Coloring graph is giving a color to a set of vertices and a set of edges on a graph. The condition for coloring a graph is that each color is different for each neighboring member graph.
Muhammad Usaid Hudloir +4 more
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RAINBOW CONNECTION PADA GRAF AMALGAMASI TANGGA SEGITIGA DIPERUMUM HOMOGEN
Jurnal Matematika UNAND, 2019 Untuk graf G terhubung dan tak trivial, dan k suatu bilangan bulat positif, misalkan c : E(G) → {1, 2, ..., k} suatu pewarnaan sisi di G, dimana sisi yang bertetangga boleh diberi warna yang sama. Suatu lintasan di G dikatakan lintasan rainbow jika tidak
Muhardiansyah Muhardiansyah +2 more
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