Additive bases of vector spaces over prime fields
Journal of Combinatorial Theory Series A
Group connectivity of graphs: a nonhomogeneous analogue of nowhere-zero flow properties
Journal of Combinatorial Theory Series B
Nowhere-zero 3-flows of highly connected graphs
Discrete Mathematics
Ore Condition and Nowhere-Zero 3-Flows
SIAM Journal on Discrete Mathematics
Nowhere-zero 3-flows in locally connected graphs
Journal of Graph Theory
Ore-condition and Z3-connectivity
European Journal of Combinatorics
Nowhere-zero 3-flows in triangularly connected graphs
Journal of Combinatorial Theory Series B
Graph Theory
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Let G be a 2-edge-connected graph of order n such that each pair of vertices x and y at distance 2 satisfies max{d(x),d(y)}n2 (weak Fan-condition, [G.H. Fan, New sufficient conditions for cycles in graphs, J. Combin. Theory Ser. B 37 (1984) 221-227]). It is obtained in this paper that G admits a nowhere-zero 3-flow and is a 3-flow contractible configuration except for a family of well-characterized counterexamples. This result generalizes some earlier results about 3-flows, 3-flow contractible configurations under some degree-sum conditions ([G. Fan, C. Zhou, Ore condition and nowhere-zero 3-flows, SIAM J. Discrete Math. 22 (2008) 288-294], [R. Luo, R. Xu, J.H. Yin, G.X. Yu, Ore-condition and Z"3-connectivity, European J. Combin. 29 (2008) 1587-1595]).