1Sharif University of Technology 2Department of Engineering Science, College of Engineering, University of Tehran 3School of Mathematics, Institute for Research in Fundamental Sciences (IPM) 4Department of Mathematical Sciences, Amirkabir University of Technology
The electronic journal of combinatorics, Tome 19 (2012) no. 2
Let $G$ be a graph. A zero-sum flow of $G$ is an assignment of non-zero real numbers to the edges of $G$ 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 $\{\pm 1,\ldots ,\pm(k-1)\}$. It has been conjectured that every $r$-regular graph, $r\geq 3$, admits a zero-sum $5$-flow. In this paper we provide an affirmative answer to this conjecture, except for $r=5$.
1
Sharif University of Technology
2
Department of Engineering Science, College of Engineering, University of Tehran
3
School of Mathematics, Institute for Research in Fundamental Sciences (IPM)
4
Department of
Mathematical Sciences, Amirkabir University of Technology
@article{10_37236_2145,
author = {Saieed Akbari and Narges Ghareghani and Gholamreza Khosrovshahi and Sanaz Zare},
title = {A note on zero-sum 5-flows in regular graphs},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {2},
doi = {10.37236/2145},
zbl = {1243.05100},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2145/}
}
TY - JOUR
AU - Saieed Akbari
AU - Narges Ghareghani
AU - Gholamreza Khosrovshahi
AU - Sanaz Zare
TI - A note on zero-sum 5-flows in regular graphs
JO - The electronic journal of combinatorics
PY - 2012
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%A Sanaz Zare
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%J The electronic journal of combinatorics
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%U http://geodesic.mathdoc.fr/articles/10.37236/2145/
%R 10.37236/2145
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Saieed Akbari; Narges Ghareghani; Gholamreza Khosrovshahi; Sanaz Zare. A note on zero-sum 5-flows in regular graphs. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2145
