Tutte's $3$-Flow Conjecture in $3$-tree-connected graphs

Morteza Hasanvand

Tutte's $3$-Flow Conjecture in $3$-tree-connected graphs

Combinatorics 2022-05-16 v2

Authors: Morteza Hasanvand

Abstract

Tutte's $3$ -flow conjecture says that every $4$ -edge-connected graph admits a nowhere-zero $3$ -flow. Kochol (2001) showed that it is enough to prove this conjecture for $5$ -edge-connected graphs. Former, Jaeger, Linial, Payan, and Tarsi (1992) conjectured that every $5$ -edge-connected graph is $Z_3$ -connected and so it admits a nowhere-zero $3$ -flow. In this note, we show that if the second conjecture would be true, then every $3$ -tree-connected graph must also be $Z_3$ -connected and so Tutte's $3$ -flow conjecture can be extended to this family of graphs.

Keywords

hadwiger conjecture graph theory

Cite

@article{arxiv.1611.02231,
  title  = {Tutte's $3$-Flow Conjecture in $3$-tree-connected graphs},
  author = {Morteza Hasanvand},
  journal= {arXiv preprint arXiv:1611.02231},
  year   = {2022}
}

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