Nowhere zero ows in line graphs
Zhi‐Hong Chen, Hong‐Jian Lai, Hongyuan Lai · 2001
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-ow would imply that L(G), the line graph of G, also has a nowhere zero k-ow. The validity of Tutte’s ow conjectures on line graphs would also imply the truth of these conjectures in general. c 2001 Elsevier Science B.V. All rights reserved.