On three zero-sum Ramsey-type problems
نویسندگان
چکیده
For a graph G whose number of edges is divisible by k, let R(G,Zk) denote the minimum integer r such that for every function f : E(Kr) 7→ Zk there is a copy G′ of G in Kr so that ∑ e∈E(G′) f(e) = 0 (in Zk). We prove that for every integer k, R(Kn, Zk) ≤ n + O(k log k) provided n is sufficiently large as a function of k and k divides ( n 2 ) . If, in addition, k is an odd prime-power then R(Kn, Zk) ≤ n + 2k − 2 and this is tight if k is a prime that divides n. A related result is obtained for hypergraphs. It is further shown that for every graph G on n vertices with an even number of edges R(G,Z2) ≤ n+ 2. This estimate is sharp. ∗Research supported in part by a United States Israel BSF Grant and by a Bergmann Memorial Grant
منابع مشابه
Diagonal Forms, Linear Algebraic Methods and Ramsey-Type Problems
This thesis focuses mainly on linear algebraic aspects of combinatorics. Let Nt(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of Nt(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H. As a continu...
متن کاملA Complete Characterization of the Zero-Sum (mod 2) Ramsey Numbers
THEOREM. Let G be a graph on n vertices and an euen number of edges. Then the zero-sum (mod 2) Ramsey numbers are given by {i +2 R(G, ~2) = + 1 +t ifG=Kn, n =0,1(mod4) if all the degrees in G are odd otherwise. 0 (mod 2) This settles several problems raised mainly by Noga Alon, Arie Bialostocki, and Yehuda Roditty.
متن کاملSome Problems in View of Recent Developments of the Erdős Ginzburg Ziv Theorem
Two conjectures concerning the Erdős Ginzburg Ziv theorem were recently confirmed. Reiher and di Fiore proved independently the two dimension analogue of the EGZ theorem, as conjectured by Kemnitz, and Grynkiewicz proved the weighed generalization of the EGZ theorem as conjectured by Caro. These developments trigger some further problems. First, we will present computer experiments that at leas...
متن کاملZero-sum Dynamic Games and a Stochastic Variation of Ramsey Theorem
We show how a stochastic variation of Ramsey theorem can be used to prove the existence of the value, and to construct ε-optimal strategies, in two-player zero-sum dynamic games that have certain properties.
متن کاملA generalization of a Ramsey-type theorem on hypermatchings
For an r-uniform hypergraph G define N(G, l; 2) (N(G, l;Zn)) as the smallest integer for which there exists an r-uniform hypergraph H on N(G, l; 2) (N(G, l;Zn)) vertices with clique(H)< l such that every 2-coloring (Zn-coloring) of the edges of H implies a monochromatic (zero-sum) copy of G. Our results strengthen a Ramsey-type theorem of Bialostocki and Dierker on zero-sum hypermatchings. As a...
متن کاملMultiple attribute decision making with triangular intuitionistic fuzzy numbers based on zero-sum game approach
For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value ind...
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 17 شماره
صفحات -
تاریخ انتشار 1993