Conjectured circular-flow bound for odd-regular graphs

Let t>1t>1 be an integer and let GG be a (2t+1)(2t+1)-graph, meaning a graph in which every vertex has degree 2t+12t+1. The odd-regular flow conjecture. Every such graph satisfies

Fc(G)2+2t.F_c(G)\leq 2+\frac{2}{t}.

The source presents this as a possible extension of the statement equivalent to Tutte's 3-flow conjecture for 55-graphs; it would imply the accompanying conjecture for class 1 graphs and remains open in the stated range.

Sources & referencesView supporting material

Primary source

Eckhard Steffen, “Edge-colorings and circular flow numbers on regular graphs”, arXiv:1310.8441 (2013).

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