Nowhere zero flows in line graphs
Cai an Corneil (Discrete Math. 102 (1992) 103–106), proved that if a graph has a cycle double cover, then its line graph also has a cycle double cover, and that the validity of the cycle double cover conjecture on line graphs would imply the truth of the conjecture in general. In this note we investigate the conditions under which a graph G has a nowhere zero k-flow would imply that L(G), the line graph of G, also has a nowhere zero k-flow. The validity of Tutte's flow conjectures on line graphs would also imply the truth of these conjectures in general.
Chen, Zhi-Hong; Lai, Hong-Jian; and Lai, Hongyuan, "Nowhere zero flows in line graphs" Discrete Mathematics 230/1 (2001): 133-141.
Available at https://digitalcommons.butler.edu/facsch_papers/1180