Results 21 to 30 of about 96,099 (217)
Jambura Journal of Mathematics, 2022 Rainbow vertex-connection number is the minimum k-coloring on the vertex graph G and is denoted by rvc(G). Besides, the rainbow-vertex connection number can be applied to some special graphs, such as prism graph and path graph.
Indrawati Lihawa +5 more
doaj +1 more source
The Vertex-Rainbow Connection Number of Some Graph Operations
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored (respectively vertex-colored) graph G is rainbow (respectively vertex-rainbow) if no two edges (respectively internal vertices) of the path are colored the same.
Li Hengzhe, Ma Yingbin, Li Xueliang
doaj +1 more source
On the threshold for rainbow connection number r in random graphs [PDF]
, 2013 We call an edge colouring of a graph G a rainbow colouring if every pair of vertices is joined by a rainbow path, i.e., a path where no two edges have the same colour.
Heckel, Annika, Riordan, Oliver
core +1 more source
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Domingos Dellamonica Jr. +2 more
openaire +1 more source
Kernels by rainbow paths in arc-colored tournaments [PDF]
Discrete Applied Mathematics, 2020 For an arc-colored digraph $D$, define its {\em kernel by rainbow paths} to be a set $S$ of vertices such that (i) no two vertices of $S$ are connected by a rainbow path in $D$, and (ii) every vertex outside $S$ can reach $S$ by a rainbow path in $D$. In this paper, we show that it is NP-complete to decide whether an arc-colored tournament has a kernel
Yandong Bai, Binlong Li, Shenggui Zhang
openaire +3 more sources
Rainbow connection number of amalgamation of some graphs
AKCE International Journal of Graphs and Combinatorics, 2016 Let G be a nontrivial connected graph. For k∈N, we define a coloring c:E(G)→{1,2,…,k} of the edges of G such that adjacent edges can be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. A rainbow path connecting
D. Fitriani, A.N.M. Salman
doaj +1 more source
Rainbow vertex pair-pancyclicity of strongly edge-colored graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 An edge-colored graph is \emph{rainbow }if no two edges of the graph have the same color. An edge-colored graph $G^c$ is called \emph{properly colored} if every two adjacent edges of $G^c$ receive distinct colors in $G^c$.
Peixue Zhao, Fei Huang
doaj +1 more source
Graphs without a rainbow path of length 3
Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, 2023 In 1959 Erd\H os and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. We investigate a rainbow version of the theorem, in which one considers $k \geq 1$ graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum ...
Sebastian Babinski, Andrzej Grzesik
openaire +4 more sources
On Rainbow Antimagic Coloring of Joint Product of Graphs
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Let be a connected graph with vertex set and edge set . A bijection from to the set is a labeling of graph . The bijection is called rainbow antimagic vertex labeling if for any two edge and in path , where and .
Brian Juned Septory +3 more
doaj +1 more source
On the fine-grained complexity of rainbow coloring [PDF]
, 2016 The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in $k$ colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors.
Kowalik, Łukasz +2 more
core +3 more sources