Girth six cubic graphs have Petersen minors
Neil Robertson, Paul Seymour, Robin Thomas
TL;DR
This paper proves that any 3-regular graph with girth at least six necessarily contains a subdivision of the Petersen graph, revealing a structural property of such graphs.
Contribution
It establishes a new characterization of 3-regular graphs with girth six by linking them to Petersen minors, a significant structural insight.
Findings
3-regular graphs with girth ≥6 contain Petersen subdivisions
Structural link between girth and Petersen minors
New characterization of certain cubic graphs
Abstract
We prove that every 3-regular graph with no circuit of length less than six has a subgraph isomorphic to a subdivision of the Petersen graph.
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