Results 191 to 200 of about 96,099 (217)

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
openaire   +1 more source

Complete graphs and complete bipartite graphs without rainbow path

Discrete Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xihe Li, Ligong Wang
exaly   +2 more sources

On the complexity of rainbow vertex colouring diametral path graphs

Journal of Computer and System Sciences
Given 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
exaly   +4 more sources

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
openaire   +1 more source

Long rainbow paths and rainbow cycles in edge colored graphs – A survey

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Spectral radius and rainbow Hamilton paths of a graph

Discrete Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaocong He, Yongtao Li, Lihua Feng
openaire   +2 more sources

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
openaire   +1 more source

The rainbow numbers of paths in maximal bipartite planar graphs

Discrete Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lei Ren, Yongxin Lan, Changqing Xu
openaire   +2 more sources

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
openaire   +2 more sources

Almost all optimally coloured complete graphs contain a rainbow Hamilton path

Journal of Combinatorial Theory Series B, 2022
Tom Kelly, Daniela Kuhn, Deryk Osthus
exaly