A list analog of Vizing's Theorem for simple graphs with triangles but   no other odd cycles
  This paper has been withdrawn by the author. Peterson and Woodall previously proved that the list-edge-colouring conjecture holds for graphs without odd cycles of length 5 or longer.   D. Peterson and D. R. Woodall, Edge-choosability in line-perfect multigraphs, Discrete Mathematics 202 (1999), 191-199.   D. Peterson and D. R. Woodall, Erratum to "Edge-choosability in line-perfect multigraphs", Discrete Mathematics 260 (2003), 323-326. 
Jessica McDonald
math.CO