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A linear forest is a kind of forest formed from the disjoint union of path graphs. The linear arboricity of a graph is the minimum number of linear forests into which the graph can be partitioned. For example, for a grid the linear arboricity is two, and the two forests are the horizontal and vertical chains.

I'm looking for an (approximative or greedy) algorithm to find such a minimal partitioning for a general graph.

Update: equally interesting would be a method to construct a "balanced" linear forest covering of the edges of a graph in the sense that each path in every forest has approximately the same length.

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    a stupid approach is to take any minimal spanning tree and remove it from the graph and then call the same algo on each of the connected components. not sure if it has a decent running time or not – 2017-02-13
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    Determining linear arboricity is NP-hard, according to [here](https://en.wikipedia.org/wiki/Linear_arboricity). So it's extremely unlikely there will be a good algorithm that actually finds a minimum partition for an arbitrary graph. – 2017-02-13
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    What about inexact algorithms which sometimes find good solutions in practice? – 2017-02-13
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    I'm not sure. Try googling "approximation algorithm linear arboricity" – 2017-02-13
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    Try reading up on tree width. It seems like a related concept. – 2017-03-23

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