Zero-Sum 6-Flows in 5-Regular Graphs
نویسندگان
چکیده
منابع مشابه
A Note on Zero-Sum 5-Flows in Regular Graphs
Let G be a graph. A zero-sum flow of G 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. Let k be a natural number. A zero-sum k-flow is a flow with values from the set {±1, . . . ,±(k − 1)}. It has been conjectured that every r-regular graph, r ≥ 3, admits a zero-sum 5-flow. In this paper we give an affirmativ...
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 کامل0-Sum and 1-Sum Flows in Regular Graphs
Let G be a graph. Assume that l and k are two natural numbers. An l-sum flow on a graph G is an assignment of non-zero real numbers to the edges of G such that for every vertex v of G the sum of values of all edges incident with v equals l. An l-sum k-flow is an l-sum flow with values from the set {±1, . . . ,±(k − 1)}. Recently, it was proved that for every r, r > 3, r 6= 5, every r-regular gr...
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: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2017
ISSN: 0126-6705,2180-4206
DOI: 10.1007/s40840-017-0547-z