On the anti-Ramsey number of forests
نویسندگان
چکیده
We call a subgraph of an edge-colored graph rainbow, if all its edges have different colors. The anti-Ramsey number G in complete K n , denoted by r ( ) is the maximum colors edge-coloring with no rainbow copy . In this paper, we determine exact value for star forests and double stars approximate linear forests.
منابع مشابه
The anti-Ramsey number of perfect matching
An r-edge coloring of a graph G is a mapping h : E(G) → [r], where h(e) is the color assigned to edge e ∈ E(G). An exact r-edge coloring is an r-edge coloring h such that there exists an e ∈ E(G) with h(e) = i for all i ∈ [r]. Let h be an edge coloring of G. We say G is rainbow if no two edges in G are assigned the same color by h. The anti-Ramsey number, AR(G,n), is the smallest integer r such...
متن کاملAnti-Ramsey number of matchings in hypergraphs
A k-matching in a hypergraph is a set of k edges such that no two of these edges intersect. The anti-Ramsey number of a k-matching in a complete s-uniform hypergraph H on n vertices, denoted by ar(n, s, k), is the smallest integer c such that in any coloring of the edges of H with exactly c colors, there is a k-matching whose edges have distinct colors. The Turán number, denoted by ex(n, s, k),...
متن کاملOn a Variation of the Ramsey Number
Let c(m, zi) be the least integer p such that, for any graph G of order p, either G has an zzi-cycle or its complement G has an zz-cycle. Values of c(m, n) are established for zzz, zi < 6 and general formulas are proved for c(3, zi), c(4, n), and c(5, zz). Introduction. It is a well-known fact that in any gathering of six people, there are three people who are mutual acquaintances or three peop...
متن کاملOn the Size-Ramsey Number of Hypergraphs
The size-Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2-edge-coloring of H yields a monochromatic copy of G. Size-Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size-Ramsey numbers for k-uniform hypergraphs. Analogous to the graph case, we cons...
متن کاملA note on the Ramsey number and the planar Ramsey number for C4 and complete graphs
We give a lower bound for the Ramsey number and the planar Ramsey number for C4 and complete graphs. We prove that the Ramsey number for C4 and K7 is 21 or 22. Moreover we prove that the planar Ramsey number for C4 and K6 is equal to 17.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2020.08.027