Nowhere-zero 3-flows in Cayley graphs on supersolvable groups

TL;DR

This paper proves Tutte's 3-flow conjecture for specific classes of Cayley graphs on supersolvable groups with certain Sylow subgroup conditions, advancing understanding of nowhere-zero 3-flows in algebraic graph theory.

Contribution

It establishes the conjecture for Cayley graphs on supersolvable groups with noncyclic Sylow 2-subgroups and on groups with square-free derived subgroups, extending previous results.

Findings

Proves Tutte's 3-flow conjecture for Cayley graphs on supersolvable groups with specific Sylow subgroup conditions.

Demonstrates the conjecture holds for Cayley graphs on groups with square-free derived subgroup.

Advances the understanding of nowhere-zero 3-flows in algebraic graph theory.

Abstract

Tutte's 3-flow conjecture asserts that every $4$-edge-connected graph admits a nowhere-zero $3$-flow. We prove that this conjecture is true for every Cayley graph of valency at least four on any supersolvable group with a noncyclic Sylow $2$-subgroup and every Cayley graph of valency at least four on any group whose derived subgroup is of square-free order.