Decomposing a planar graph with girth 9 into a forest and a matching (Q925026)
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scientific article; zbMATH DE number 5280763
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decomposing a planar graph with girth 9 into a forest and a matching |
scientific article; zbMATH DE number 5280763 |
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Decomposing a planar graph with girth 9 into a forest and a matching (English)
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29 May 2008
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A decomposition of a graph is a partitioning of the edge set. The authors show that any planar graph of girth 9 has a decomposition such that one part is a forest and the second part is a matching. This was previously known for planar graphs of girth 11, subsequently improved to girth 10. It is an open question if any planar graph of girth 8 decomposes into a forest and a matching. This is related to results such as a planar graph of girth 6 can be decomposed into a forest and a graph with maximum degree 2, and a planar graph can be decomposed into 3 forests such that one forest has maximum degree at most 8.
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decomposition
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planar
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