Abstract
We prove that for an undirected graph with arboricity at most k + ε, its edges can be decomposed into k forests and a subgraph with maximum degree \(\lceil \frac{k \epsilon +1}{1-\epsilon} \rceil\). The problem is solved by a linear programming based approach: we first prove that there exists a fractional solution to the problem, and then use a result on the degree bounded matroid problem by Király, Lau and Singh [5] to get an integral solution.
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References
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Király, T., Lau, L.C. (2011). Degree Bounded Forest Covering. In: Günlük, O., Woeginger, G.J. (eds) Integer Programming and Combinatoral Optimization. IPCO 2011. Lecture Notes in Computer Science, vol 6655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20807-2_25
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DOI: https://doi.org/10.1007/978-3-642-20807-2_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20806-5
Online ISBN: 978-3-642-20807-2
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