Treelike snarks
Mari\'en Abreu, Tomas Kaiser, Domenico Labbate, Giuseppe Mazzuoccolo
TL;DR
This paper introduces a new infinite family of treelike snarks with specific edge-covering properties, proving they have circular flow number five and admit a 5-cycle double cover, using computer-assisted methods.
Contribution
It constructs a novel infinite family of treelike snarks with unique properties, expanding the understanding of snark structures and their flow and covering characteristics.
Findings
The family has circular flow number five.
They admit a 5-cycle double cover.
Construction is supported by computer-assisted proof.
Abstract
We study snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hagglund. We construct another infinite family, arising from a generalisation in a different direction. The proof that this family has the requested property is computer-assisted. In addition, we prove that the snarks from this family (we call them treelike snarks) have circular flow number five and admit a 5-cycle double cover.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Computational Geometry and Mesh Generation · Limits and Structures in Graph Theory