Local Ramsey numbers for linear forests
نویسندگان
چکیده
Let L be a disjoint union of nontrivial paths. Such a graph we call a linear forest. We study the relation between the 2-local Ramsey number R2-loc(L) and the Ramsey number R(L), where L is a linear forest. L will be called an (n, j)-linear forest if L has n vertices and j maximal paths having an odd number of vertices. If L is an (n, j)-linear forest, then R2-loc(L) = (3n − j)/2 + dj/2e −
منابع مشابه
A generalization of Ramsey theory for linear forests
Chung and Liu defined the d-chromatic Ramsey numbers as a generalization of Ramsey numbers by replacing a weaker condition. Let 1 < d < c and let t = (c d ) . Assume A1, A2, . . . , At are all d-subsets of a set containing c distinct colors. Let G1, G2, . . . , Gt be graphs. The d-chromatic Ramsey number denoted by rc d(G1, G2, . . . , Gt) is defined as the least number p such that, if the edge...
متن کاملZarankiewicz Numbers and Bipartite Ramsey Numbers
The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...
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 کاملRestricted size Ramsey number for path of order three versus graph of order five
Let G and H be simple graphs. The Ramsey number r(G,H) for a pair of graphs G and H is the smallest number r such that any red-blue coloring of the edges of Kr contains a red subgraph G or a blue subgraph H . The size Ramsey number r̂(G,H) for a pair of graphs G and H is the smallest number r̂ such that there exists a graph F with size r̂ satisfying the property that any red-blue coloring of the e...
متن کاملMinimal Ordered Ramsey Graphs
An ordered graph is a graph equipped with a linear ordering of its vertex set. A pair of ordered graphs is Ramsey finite if it has only finitely many minimal ordered Ramsey graphs and Ramsey infinite otherwise. Here an ordered graph F is an ordered Ramsey graph of a pair (H,H ′) of ordered graphs if for any coloring of the edges of F in colors red and blue there is either a copy of H with all e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005