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.
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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.
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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
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DOI: https://doi.org/10.1007/s00373-002-0504-x