Elsevier

Discrete Applied Mathematics

Volume 257, 31 March 2019, Pages 350-352
Discrete Applied Mathematics

Note
Equivalent versions of group-connectivity theorems and conjectures

https://doi.org/10.1016/j.dam.2018.10.010Get rights and content
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Abstract

We present equivalent versions of conjecture of Jaeger, Linial, Payan, and Tarsi from 1992 that every 5-edge-connected graph is Z3-connected and theorem of Lovász, Thomassen, Wu, and Zhang from 2013 that every 6-edge-connected graph is Z3-connected. In particular, we prove that every (6,4,3,3)-edge-connected graph is Z3-connected (a graph G is (k,k1,,kn)-edge-connected, k>k1kn, if G has an ordered set of vertices U=(u1,,un) such that each edge-cut that separates ui from U{ui} has cardinality at least ki, i=1,,n, and all other edge-cuts of G have cardinality at least k).

Keywords

Z3-flow
Z3-connectivity
Edge-connectivity
Edge-critical set
Superposition

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