Abstract.
Let G be a planar graph with maximum degree Δ and girth g. The linear 2-arboricity la 2(G) of G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose component trees are paths of length at most 2. We prove that (1) la 2(G)≤⌈(Δ+1)/2⌉+12; (2) la 2(G)≤⌈(Δ+1)/2⌉+6 if g≥4; (3) la 2(G)≤⌈(Δ+1)/2⌉+2 if g≥5; (4) la 2(G)≤⌈(Δ+1)/2⌉+1 if g≥7.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: June 28, 2001 Final version received: May 17, 2002
Acknowledgments. This work was done while the second and third authors were visiting the Institute of Mathematics, Academia Sinica, Taipei. The financial support provided by the Institute is greatly appreciated.
Rights and permissions
About this article
Cite this article
Lih, KW., Tong, LD. & Wang, WF. The Linear 2-Arboricity of Planar Graphs. Graphs and Combinatorics 19, 241–248 (2003). https://doi.org/10.1007/s00373-002-0504-x
Issue Date:
DOI: https://doi.org/10.1007/s00373-002-0504-x