A graph is $(7,2)$-edge-choosable if, for every assignment of lists of size $7$ to the edges, it is possible to choose $2$ colors for each edge from its list so that no color is chosen for two incident edges. We show that every $3$-edge-colorable graph is $(7,2)$-edge-choosable and also that many non-$3$-edge-colorable $3$-regular graphs are $(7,2)$-edge-choosable.
['Daniel W. Cranston', 'Douglas B. West']
Classes of 3-Regular Graphs That Are (7, 2)-Edge-Choosable