List linear arboricity of planar graphs
Xinhui An, Baoyindureng Wu · Discussiones Mathematicae Graph Theory · 2009
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We conrm that this conjecture is true for any planar graph having > 13, or for any planar graph with > 7 and without i-cycles for some i 2 f3; 4; 5g. We also prove that d ( G) 2 e 6 lla(G) 6 d ( G)+1 2 e for any planar graph having > 9.