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A snark is a graph that is connected, regular of degree 3, bridgeless, but has edge chromatic number 4. The fractional edge chromatic number is therefore between 3 and 4. I have checked several and all cases have fractional edge chromatic number 3. So: Is it the case that all snarks have fractional edge chromatic number 3?

Stan Wagon

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$\chi_f(G)$ = $\max (\Delta (G), \Lambda (G))$, where $\Lambda (G)$ = $\max_H \frac{2\epsilon(H)}{\nu(H) − 1}$ where the maximization is over all induced subgraphs $H$ with $\nu(H) ≥ 3$ and odd. For Snarks, $\Lambda (G) \leq 3$. For more details check the chapter on edge coloring in Fractional Graph Theory.

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Excellent. Many thanks. –  stan wagon May 28 '12 at 14:44

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