Theory of linear and integer programming
Theory of linear and integer programming
Enumerative combinatorics
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Handbook of combinatorics (vol. 1)
Convex polytopes and related complexes
Handbook of combinatorics (vol. 1)
Superposition and constructions of graphs without nowhere-zero k-flows
European Journal of Combinatorics
Graph Theory With Applications
Graph Theory With Applications
Hypothetical complexity of the nowhere-zero 5-flow problem
Journal of Graph Theory
Zero-Free Intervals for Flow Polynomials of Near-Cubic Graphs
Combinatorics, Probability and Computing
The number of nowhere-zero flows on graphs and signed graphs
Journal of Combinatorial Theory Series B
Bounds on the coefficients of tension and flow polynomials
Journal of Algebraic Combinatorics: An International Journal
Enumerating colorings, tensions and flows in cell complexes
Journal of Combinatorial Theory Series A
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In this paper we study relations between nowhere-zero Zk and integer-valued flows in graphs and the functions FG(k) and IG(k) evaluating the numbers of nowhere-zero Zk- and k-flows in a graph G, respectively. It is known that FG(k) is a polynomial for k 0. We show that IG(k) is also a polynomial and that 2m(G)FG(k) ≥ IG(k) ≥ (m(G)+1) FG(k), where m(G) is the rank of the cocycle matroid of G. Finally we prove that FG(k+ 1) ≥ FG(k) . k/(k-1) and IG(k+ 1) ≥ IG(k) . k/(k-1) for every k 1.