Subdivided graphs have linear ramsey numbers
نویسنده
چکیده
It is shown that the Ramsey number of any graph with n vertices in which no two vertices of degree at least 3 are adjacent is at most 12n. In particular, the above estimate holds for the Ramsey number of any n-vertex subdivision of an arbitrary graph, provided each edge of the original graph is subdivided at least once. This settles a problem of Burr and Erdös.
منابع مشابه
3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
Chvátal, Rödl, Szemerédi and Trotter [1] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform ‘pseudo-random’ hypergraphs. keywords: hypergraphs; regularity lemm...
متن کاملRamsey numbers of ordered graphs
An ordered graph G< is a graph G with vertices ordered by the linear ordering <. The ordered Ramsey number R(G<, c) is the minimum number N such that every ordered complete graph with c-colored edges and at least N vertices contains a monochromatic copy of G<. For unordered graphs it is known that Ramsey numbers of graphs with degrees bounded by a constant are linear with respect to the number ...
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 کاملOn the Ramsey numbers for linear forest versus some graphs
For given graphs G and H; the Ramsey number R(G;H) is the leastnatural number n such that for every graph F of order n the followingcondition holds: either F contains G or the complement of F contains H.In this paper firstly, we determine Ramsey number for union of pathswith respect to sunflower graphs, For m ≥ 3, the sunflower graph SFmis a graph on 2m + 1 vertices obtained...
متن کاملRamsey numbers for bipartite graphs with small bandwidth
We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. In particular we determine asymptotically the two and three color Ramsey numbers for grid graphs. More generally, we determine the two color Ramsey number for bipartite graphs with small bandwidth and bounded maximum degree and the three color Ramsey number for such graphs with the additional assump...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 18 شماره
صفحات -
تاریخ انتشار 1994