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

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

doi:10.1016/j.ejc.2011.09.041

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

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

Penn State Scranton

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	182-188
Number of pages	7
Journal	European Journal of Combinatorics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1016/j.ejc.2011.09.041
State	Published - Feb 2012

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2011.09.041

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title = "Z3-connectivity of 4-edge-connected 2-triangular graphs",

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.",

author = "Xinmin Hou and Lai, \{Hong Jian\} and Mingquan Zhan and Taoye Zhang and Ju Zhou",

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AU - Lai, Hong Jian

AU - Zhan, Mingquan

AU - Zhang, Taoye

AU - Zhou, Ju

PY - 2012/2

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AB - 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.

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ER -

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

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