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

Authors:
Xinmin Hou;Hong-Jian Lai;Mingquan Zhan;Taoye Zhang;Ju Zhou
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, 230026, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China and Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA;Department of Mathematics, Millersville University, Millersville, PA 17551, USA;Department of Mathematics, Penn State University, Dunmore, PA 18512, USA;Department of Mathematics, Kutztown University, Kutztown, PA 19530, USA
Venue:
European Journal of Combinatorics
Year:
2012

Citing 4
Cited 1

Group connectivity of graphs: a nonhomogeneous analogue of nowhere-zero flow properties

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications
On Group Connectivity of Graphs

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Nowhere-zero 3-flows in triangularly connected graphs

Journal of Combinatorial Theory Series B

Nowhere-zero 3-flows and modulo k-orientations

Journal of Combinatorial Theory Series B

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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 Z"3-flow. However, it has been proved that not all such graphs are Z"3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z"3-connected. The result is best possible. This result provides evidence to support the Z"3-connectivity conjecture by Jaeger et al that every 5-edge-connected graph is Z"3-connected.