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Partitioning a planar graph of girth 10 into a forest and a matching. (English) Zbl 1209.05062

Summary: We prove that any finite planar graph with girth at least 10 can have its edges partitioned to form two graphs on the same vertices, one of which is a forest, and the other of which is a matching. Several related results are also demonstrated.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C05 Trees
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References:

[1] He, Edge partitions of planar graphs and their game coloring numbers, J. Graph Theory 41 pp 307– (2002) · Zbl 1016.05033
[2] Borodin, Decomposing a planar graph with girth nine into a forest and a matching, Eur. J. Combin. 29 pp 1235– (2008) · Zbl 1144.05019
[3] 3. S.-Y. Ho and D. J. Kleitman , Planar graph decomposition of Girth Six, to appear.
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[5] Borodin, Minimax degrees of quasiplane graphs without 4-faces, Siberian Electronic Math. 4 pp 435– (2007) · Zbl 1132.05312
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