Results 1 to 10 of about 1,117,749 (247)
On kernels by rainbow paths in arc-coloured digraphs [PDF]
Open Mathematics, 2021 In 2018, Bai, Fujita and Zhang [Discrete Math. 341 (2018), no. 6, 1523–1533] introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph DD, which is a subset SS of vertices of DD such that (aa) there exists no ...
Li Ruijuan, Cao Yanqin, Zhang Xinhong
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A note on rainbow mean indexes of paths [PDF]
Discrete Mathematics Letters, 2021 Summary: For an edge coloring of a connected graph \(G\) of order 3 or more with positive integers, the chromatic mean of a vertex \(v\) of \(G\) is defined as that vertex color which is the average of the colors of the edges incident with \(v\). Only those edge colorings \(c\) for which the chromatic mean of every vertex is a positive integer are ...
Gary Chartrand +3 more
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On the complexity of rainbow vertex colouring diametral path graphs
Journal of Computer and System SciencesGiven a graph and a colouring of its vertices, a rainbow vertex path is a path between two vertices such that all the internal nodes of the path are coloured distinctly. A graph is rainbow vertex-connected if between every pair of vertices in the graph there exists a rainbow vertex path.
Dyrseth, Jakob, Thomé de Lima, Paloma
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Rainbow Paths and Large Rainbow Matchings [PDF]
The Electronic Journal of Combinatorics, 2022 A conjecture of the first two authors is that $n$ matchings of size $n$ in any graph have a rainbow matching of size $n-1$. We prove a lower bound of $\frac{2}{3}n-1$, improving on the trivial $\frac{1}{2}n$, and an analogous result for hypergraphs. For $\{C_3,C_5\}$-free graphs and for disjoint matchings we obtain a lower bound of $\frac{3n}{4}-O(1)
Ron Aharoni +3 more
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Rainbow Connection Numbers of WK-Recursive Networks and WK-Recursive Pyramids
MathematicsAn edge coloring of a graph G results in G being rainbow connected when every pair of vertices is linked by a rainbow path. Such a path is defined as one where each edge possesses a distinct color.
Fu-Hsing Wang, Cheng-Ju Hsu
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Barekeng, 2023 Rainbow antimagic coloring is a combination of antimagic labeling and rainbow coloring. Antimagic labeling is labeling of each vertex of the graph with a different label, so that each the sum of the vertices in the graph has a different weight. Rainbow
R Adawiyah +4 more
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Gallai–Ramsey Numbers for Rainbow Paths [PDF]
Graphs and Combinatorics, 2020 Given graphs $G$ and $H$ and a positive integer $k$, the \emph{Gallai-Ramsey number}, denoted by $gr_{k}(G : H)$ is defined to be the minimum integer $n$ such that every coloring of $K_{n}$ using at most $k$ colors will contain either a rainbow copy of $G$ or a monochromatic copy of $H$. We consider this question in the cases where $G \in \{P_{4}, P_{5}
Xihe Li +4 more
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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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On the Rainbow Turán number of paths [PDF]
The Electronic Journal of Combinatorics, 2019 Let $F$ be a fixed graph. The rainbow Turán number of $F$ is defined as the maximum number of edges in a graph on $n$ vertices that has a proper edge-coloring with no rainbow copy of $F$ (i.e., a copy of $F$ all of whose edges have different colours). The systematic study of such problems was initiated by Keevash, Mubayi, Sudakov and Verstraëte.
Beka Ergemlidze +2 more
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Rainbow connection number of Cm o Pn and Cm o Cn
Indonesian Journal of Combinatorics, 2020 Let G = (V(G),E(G)) be a nontrivial connected graph. A rainbow path is a path which is each edge colored with different color. A rainbow coloring is a coloring which any two vertices should be joined by at least one rainbow path.
Alfi Maulani +3 more
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