Zero-sum partition theorems for graphs
نویسندگان
چکیده
منابع مشابه
Generalizations of Some Zero-sum Theorems
For a finite abelian group G and a finite subset A ⊆ Z, the Davenport constant of G with weight A, denoted by DA(G), is defined to be the smallest positive integer k such that for any sequence (x1, . . . , xk) of k elements in G there exists a non-empty subsequence (xj1 , . . . , xjr) and a1, . . . , ar ∈ A such that ∑r i=1 ai xji = 0. To avoid trivial cases, one assumes that the weight set A d...
متن کاملZero-Sum Flows in Regular Graphs
For an undirected graph G, a zero-sum flow is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph G has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet’s Conjecture for bidirected graphs are equivalent. Among other results it is shown that...
متن کاملOn zero-sum 6-flows of graphs
Article history: Received 20 October 2008 Accepted 21 January 2009 Available online 6 March 2009 Submitted by R.A. Brualdi AMS classification: 05C20 05C50 05C78
متن کاملZero-Sum Flow Numbers of Regular Graphs
As an analogous concept of a nowhere-zero flow for directed graphs, we consider zero-sum flows for undirected graphs in this article. For an undirected graph G, a zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum k-flow if the values of edges are less than k. We define the zer...
متن کاملTauberian theorems for sum sets
Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...
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: International Journal of Mathematics and Mathematical Sciences
سال: 1994
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171294000992