Results 21 to 30 of about 2,084 (327)
Bounds on coloring trees without rainbow paths [PDF]
Discussiones Mathematicae Graph TheoryWayne Goddard +2 more
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Rainbow-free 3-colorings in abelian groups [PDF]
Electronic Notes in Discrete Mathematics, 2009 A 3–coloring of an abelian group G is rainbow–free if there is no 3–term arithmetic progression with its members having pairwise distinct colors. We describe the structure of rainbow–free colorings of abelian groups. This structural description proves
Serra Albó, Oriol, Montejano, Amanda
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Journal of Combinatorics, 2011 Given a graph H, we denote by C(n,H) the minimum number k such that the following holds. There are n colorings of E(Kn) with k-colors, each associated with one of the vertices of Kn, such that for every copy T of H in Kn, at least one of the colorings that are associated with V (T ) assigns distinct colors to all the edges of E(T ). We characterize the
Noga Alon, Ido Ben‐Eliezer
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Rainbow degree-jump coloring of graphs
Karpatsʹkì Matematičnì Publìkacìï, 2021 In this paper, we introduce a new notion called the rainbow degree-jump coloring of a graph. For a vertex $v\in V(G)$, let the degree-jump closed neighbourhood of a vertex $v$ be defined as $N_{deg}[v] = \{u:d(v,u)\leq d(v)\}.$ A proper coloring of a ...
E.G. Mphako-Banda, J. Kok, S. Naduvath
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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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Rainbow Triangles in Arc-Colored Tournaments [PDF]
Graphs and Combinatorics, 2021 Let $T_{n}$ be an arc-colored tournament of order $n$. The maximum monochromatic indegree $Δ^{-mon}(T_{n})$ (resp. outdegree $Δ^{+mon}(T_{n})$) of $T_{n}$ is the maximum number of in-arcs (resp. out-arcs) of a same color incident to a vertex of $T_{n}$.
Wei Li +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 $n>5$.
Dhruv Mubayi, Randall Stading
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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 of $G$ lies on a full $f$-rainbow path, which provides a positive answer to a question posed by Lin ...
Oliver Bendele, Dieter Rautenbach
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Local Rainbow Colorings for Various Graphs [PDF]
The Electronic Journal of CombinatoricsMotivated by a problem in theoretical computer science suggested by Wigderson, Alon and Ben-Eliezer studied the following extremal problem systematically one decade ago. Given a graph $H$, let $C(n,H)$ be the minimum number $k$ such that the following holds. There are $n$ colorings of $E(K_{n})$ with $k$ colors, each associated with one of the vertices
Xinbu Cheng, Zixiang Xu
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Computing Minimum Rainbow and Strong Rainbow Colorings of Block Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A path in an edge-colored graph $G$ is rainbow if no two edges of it are colored the same. The graph $G$ is rainbow-connected if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph $G$ is strongly rainbow-connected.
Melissa Keranen, Juho Lauri
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