Results 1 to 10 of about 123 (118)
Algorithms for the rainbow vertex coloring problem on graph classes
Theoretical Computer Science, 2021 Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the Rainbow Vertex Coloring (RVC) problem we want to decide whether the vertices of a given graph can be colored with at ...
Paloma T Lima +2 more
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On the rainbow antimagic coloring of vertex amalgamation of graphs
Journal of Physics: Conference Series, 2022 Abstract The purpose of this study is to develop rainbow antimagic coloring. This study is a combination of two notions, namely antimagic and rainbow concept. If every vertex of graph G is labeled with the antimagic labels and then edge weight of antimagic labels are used to assign a rainbow coloring.
J C Joedo +4 more
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The rainbow vertex antimagic coloring of tree graphs
Journal of Physics: Conference Series, 2022 AbstractLetG(V(G),E(G)) be a connected, simple, and finite graph. Letfbe a bijective function of labeling on graphGfrom the edge setE(G) to natural number up to the number of edges ofG. A rainbow vertex antimagic labeling of graphGis a functionfunder the condition all internal vertices of a pathu–υ, Ɐu, υ∈V(G) have different weight (denoted byw(u ...
Ika Hesti Agustin, Elsa Yuli Kurniawati
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On Rainbow Vertex Antimagic Coloring of Shell Related Graphs
Advances in physics research, 2023 Arika Indah Kristiana +1 more
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On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion [PDF]
CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2021 All graph in this paper are simple, finite, and connected. Let be a labeling of a graph . The function is called antimagic rainbow edge labeling if for any two vertices and , all internal vertices in path have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by for every .
Marsidi Marsidi +3 more
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Rainbow Induced Subgraphs in Proper Vertex Colorings [PDF]
Fundamenta Informaticae, 2011 Given a graph H we define ρ(H) to be the minimum order of a graph G such that every proper vertex coloring of G contains a rainbow induced subgraph isomorphic to H. We give upper and lower bounds for ρ(H), compute the exact value for some classes of graphs, and consider an interesting combinatorial problem connected with computation of ρ(H) for paths ...
Andrzej Kisielewicz 0001, Marek Szykula
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Avoiding Rainbow Induced Subgraphs in Vertex-Colorings [PDF]
The Electronic Journal of Combinatorics, 2008 For a fixed graph $H$ on $k$ vertices, and a graph $G$ on at least $k$ vertices, we write $G\longrightarrow H$ if in any vertex-coloring of $G$ with $k$ colors, there is an induced subgraph isomorphic to $H$ whose vertices have distinct colors. In other words, if $G\longrightarrow H$ then a totally multicolored induced copy of $H$ is unavoidable in any
Maria Axenovich, Ryan R. Martin
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Rainbow vertex pair-pancyclicity of strongly edge-colored graphs
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 $G^c$. A \emph{strongly edge-colored} graph is a proper edge-colored graph such that every path of length $3$ is rainbow.
Peixue Zhao, Fei Huang
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Vertex-disjoint rainbow triangles in edge-colored graphs
Discrete Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jie Hu, Hao Li 0002, Donglei Yang
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Vertex rainbow colorings of graphs
Discussiones Mathematicae Graph Theory, 2012 In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P. If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a ...
Futaba Fujie-Okamoto +3 more
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