Z3-connectivity of 4-edge-connected 2-triangular graphs

Xinmin Hou, Hong Jian Lai, Mingquan Zhan, Taoye Zhang, Ju Zhou

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Abstract

A graph G is k-triangular if each edge of G is in at least k triangles. It is conjectured that every 4-edge-connected 1-triangular graph admits a nowhere-zero Z3-flow. However, it has been proved that not all such graphs are Z3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z3-connected. The result is best possible. This result provides evidence to support the Z3-connectivity conjecture by Jaeger et al. that every 5-edge-connected graph is Z3-connected.

Original languageEnglish (US)
Pages (from-to)182-188
Number of pages7
JournalEuropean Journal of Combinatorics
Volume33
Issue number2
DOIs
StatePublished - Feb 1 2012

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All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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