Group connectivity under 3‐edge‐connectivity
نویسندگان
چکیده
منابع مشابه
Forbidden graphs and group connectivity
Many researchers have devoted themselves to the study of nowhere-zero flows and group connectivity. Recently, Thomassen confirmed the weak 3-flow conjecture, which was further improved by Lovász, Thomassen, Wu and Zhang who proved that every 6-edge-connected graph is Z3-connected. However, Conjectures 1 and 2 are still open. Conjecture 2 implies Conjecture 1 by a result of Kochol that reduces C...
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Let G be an undirected graph, A be an (additive) abelian group and A∗ = A−{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V (G) → A satisfying ∑v∈V (G) b(v) = 0, there is a function f : E(G) → A∗ such that ∑e∈E+(v) f(e) − ∑ e∈E−(v) f(e) = b(v). For an abelian group A, let 〈A〉 be the family of graphs that are A-connected. The group connectivity number ...
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Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero Z3-flow and Jaeger et al. [Group connectivity of graphs–a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin. Theory Ser. B 56 (1992) 165-182] further conjectured that every 5-edge-connected graph isZ3-connected.These two conjectures are in general open and few results are known so far. Aweaker version of ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2020
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22623