منابع مشابه
Tripartite Ramsey numbers for paths
In this article, we study the tripartite Ramsey numbers of paths. We show that in any two-coloring of the edges of the complete tripartite graph K(n, n, n) there is a monochromatic path of length (1− o(1))2n. Since R(P2n+1,P2n+1) = 3n, this means that the length of the longest monochromatic path is about the same when two-colorings of K3n and K(n, n, n) are considered. © 2007 Wiley Periodicals,...
متن کاملBipartite rainbow Ramsey numbers
Let G and H be graphs. A graph with colored edges is said to be monochromatic if all its edges have the same color and rainbow if no two of its edges have the same color. Given two bipartite graphs G1 and G2, the bipartite rainbow ramsey number BRR(G1; G2) is the smallest integer N such that any coloring of the edges of KN;N with any number of colors contains a monochromatic copy of G1 or a rai...
متن کاملRainbow Paths with Prescribed Ends
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 C7, then there is a χ(G)-coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose colors are different. In [S. Akbari, V. Liaghat, and A. Nikzad. Colorful paths in vertex coloring of...
متن کاملOn Rainbow Cycles and Paths
In a properly edge colored graph, a subgraph using every color at most once is called rainbow. In this thesis, we study rainbow cycles and paths in proper edge colorings of complete graphs, and we prove that in every proper edge coloring of Kn, there is a rainbow path on (3/4− o(1))n vertices, improving on the previously best bound of (2n + 1)/3 from [?]. Similarly, a k-rainbow path in a proper...
متن کاملOptimal Colorings with Rainbow Paths
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 (Simple proofs of results on paths representing all colors in proper ...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2020
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-020-02175-8