Results 11 to 20 of about 96,099 (217)
Optimal Colorings with Rainbow Paths [PDF]
Graphs and Combinatorics, 2017 Let $G$ be a connected graph of chromatic number $k$. For a $k$-coloring $f$ of $G$, a full $f$-rainbow path is a path of order $k$ in $G$ whose vertices are all colored differently by $f$. We show that $G$ has a $k$-coloring $f$ such that every vertex
Bendele, Oliver, Rautenbach, Dieter
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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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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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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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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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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 Paths with Prescribed Ends [PDF]
The Electronic Journal of Combinatorics, 2011 It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if $G$ is a connected graph distinct from $C_7$, then there is a $\chi(G)$-coloring of $G$ in which every vertex $v\in V(G)$ is an initial vertex of a path $P$ with $\chi(G)$ vertices whose colors are different. In [S. Akbari,
Alishahi, Meysam +2 more
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A note on rainbow saturation number of paths [PDF]
Applied Mathematics and Computation, 2020 For a fixed graph $F$ and an integer $t$, the \dfn{rainbow saturation number} of $F$, denoted by $sat_t(n,\mathfrak{R}(F))$, is defined as the minimum number of edges in a $t$-edge-colored graph on $n$ vertices which does not contain a \dfn{rainbow copy} of $F$, i.e., a copy of $F$ all of whose edges receive a different color, but the addition of any ...
Shujuan Cao, Yuede Ma, Zhenyu Taoqiu
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The (Strong) Rainbow Connection Number of Join Of Ladder and Trivial Graph
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 Let G = (V,E) be a nontrivial, finite, and connected graph. A function c from E to {1,2,...,k},k ∈ N, can be considered as a rainbow k-coloring if every two vertices x and y in G has an x- y path.
Dinda Kartika +2 more
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On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion
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 ...
Marsidi Marsidi +3 more
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