Results 221 to 230 of about 1,117,749 (247)

From Colourful to Rainbow Paths in Graphs: Colouring the Vertices

Graphs and Combinatorics, 2021
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Christoph Brause, Stanislav Jendrol', Ingo Schiermeyer   +2 more
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Zero-path-difference rainbow holography

Optics Letters, 1985
Rainbow holography without the use of a slit has been demonstrated by combining Abramson's light-in-flight approach [Opt. Lett. 3, 121 (1978)] with Benton's rainbow technique [J. Opt. Soc. Am. 59, 1545 (A) 1969]. The system natural slit-shaped pupil whose extent and position are determined by the experimental parameters.
F, Quercioli, G, Molesini, S F, Jacobs
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Finding a monochromatic subgraph or a rainbow path

Journal of Graph Theory, 2006
AbstractFor simple graphs G and H, let f(G,H) denote the least integer N such that every coloring of the edges of KN contains either a monochromatic copy of G or a rainbow copy of H. Here we investigate f(G,H) when H = Pk. We show that even if the number of colors is unrestricted when defining f(G,H), the function f(G,Pk), for k = 4 and 5, equals the ...
András Gyárfás, Jenö Lehel, Richard H. Schelp   +2 more
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On the rainbow planar Turán number of paths

Discrete Mathematics
An edge-colored graph is said to contain a rainbow-$F$ if it contains $F$ as a subgraph and every edge of $F$ is a distinct color. The problem of maximizing edges among $n$-vertex properly edge-colored graphs not containing a rainbow-$F$, known as the rainbow Turán problem, was initiated by Keevash, Mubayi, Sudakov and Verstraëte.
Ervin Györi, Ryan R. Martin, Addisu Paulos, Casey Tompkins, Kitti Varga   +4 more
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Long rainbow paths and rainbow cycles in edge colored graphs – A survey

Applied Mathematics and Computation, 2018
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Spectral radius and rainbow Hamilton paths of a graph

Discrete Mathematics
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Xiaocong He, Yongtao Li, Lihua Feng
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Rainbow and orthogonal paths in factorizations of K_n

Journal of Combinatorial Designs, 2010
AbstractFor n even, a factorization of a complete graph Kn is a partition of the edges into n−1 perfect matchings, called the factors of the factorization. With respect to a factorization, a path is called rainbow if its edges are from distinct factors.
Gyarfas, Andras, Mhalla, Mehdi
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The rainbow numbers of paths in maximal bipartite planar graphs

Discrete Mathematics
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Lei Ren, Yongxin Lan, Changqing Xu
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Rainbow paths and trees in properly-colored graphs

2018
A graph $G$ is \textit{properly $k$-colored} if the colors $\{1,2,\dots,k\}$ are assigned to each vertex such that $u$ and $v$ have different colors if $uv$ is an edge and each color is assigned to some vertex. A \textit{rainbow $k$-path}, a \textit{rainbow $k$-star} and a \textit{rainbow $k$-tree} is a path, star or tree, respectively, on $k$ vertices
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Almost all optimally coloured complete graphs contain a rainbow Hamilton path

Journal of Combinatorial Theory Series B, 2022
Deryk Osthus, Thomas Kelly, Daniela Kuhn   +2 more
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