Fiol et al.'s oddness–resistance conjecture for snarks with empty buffer subgraph

Let GG be a snark, let ω(G)\omega(G) denote its oddness, let r(G)r(G) denote its resistance, and suppose that the buffer subgraph of GG is empty. Oddness–resistance conjecture with empty buffer subgraph.

ω(G)2r(G).\omega(G) \leq 2r(G).

The unrestricted inequality for snarks was disproved by constructing graphs with unbounded oddness and constant resistance. The proposed reformulation restricts the claim to snarks with empty buffer subgraph, but the supplied text gives no resolution for that restricted statement.

Sources & referencesView supporting material

Primary source

Imran Allie, “3-critical subgraphs of snarks”, arXiv:2201.07528 (2022).

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