Ramsey and Gallai-Ramsey Number for Wheels
نویسندگان
چکیده
Given a graph G and positive integer k, define the Gallai-Ramsey number to be minimum of vertices n such that any k-edge coloring $$K_n$$ contains either rainbow (all different colored) triangle or monochromatic copy G. Much like Ramsey numbers, numbers have gained reputation as being very difficult compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on for wheels exact value wheel 5 vertices.
منابع مشابه
The chromatic Ramsey number of odd wheels
We prove that the chromatic Ramsey number of every odd wheel W2k+1, k ≥ 2 is 14. That is, for every odd wheel W2k+1, there exists a 14-chromatic graph F such that when the edges of F are two-coloured, there is a monochromatic copy of W2k+1 in F , and no graph F with chromatic number 13 has the same property. We ask whether a natural extension of odd wheels to the family of generalized Mycielski...
متن کاملRamsey-type results for Gallai colorings
A Gallai-coloring (G-coloring) is a generalization of 2-colorings of edges of complete graphs: a G-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Here we extend some results known earlier for 2-colorings to G-colorings. We prove that in every G-coloring of Kn there exists each of the following: 1. a monochromatic double star with at...
متن کاملThe Ramsey numbers of large trees versus wheels
For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.
متن کاملThe Ramsey number of paths with respect to wheels
For graphs G and H , the Ramsey number R(G,H) is the smallest positive integer n such that every graph F of order n contains G or the complement of F contains H . For the path Pn and the wheel Wm, it is proved that R(Pn,Wm) = 2n − 1 if m is even, m 4, and n (m/2)(m − 2), and R(Pn,Wm)= 3n− 2 if m is odd, m 5, and n (m− 1/2)(m− 3). © 2005 Elsevier B.V. All rights reserved.
متن کاملOn Ramsey numbers for paths versus wheels
For two given graphs F and H, the Ramsey number R(F,H) is the smallest positive integer p such that for every graph G on p vertices the following holds: either G contains F as a subgraph or the complement of G contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Wm), where Pn is a path on n vertices and Wm is the graph obtained from a cycle on m vertices by adding a new ver...
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: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-021-02406-6