Geodesic
Decomposing a~planar graph into a~forest and a~subgraph of restricted maximum degree
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 296-299

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We disprove the conjecture of He, Hou, Lih, Shao, Wang and Zhu that every plane graph $G$ can be edge-partitioned into a forest and a subgraph of the maximum degree at most $\lceil\Delta(G)/2\rceil+1$. 
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     title = {Decomposing a~planar graph into a~forest and a~subgraph of restricted maximum degree},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {296--299},
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     volume = {4},
     year = {2007},
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O. V. Borodin; A. O. Ivanova; B. S. Stechkin. Decomposing a~planar graph into a~forest and a~subgraph of restricted maximum degree. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 296-299. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a18/