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
Borodin, O.V., Kostochka, A.V., Sheikh, N.N., Yu, G.: Decomposing a planar graph with girth 9 into a forest and a matching. European J. Combin. 29, 1235–1241 (2008)
Goncalves, D.: Covering planar graphs with forests, one having bounded maximum degree. J. Combin. Theory Ser. B 99, 314–322 (2009)
Kaiser, T., Montassier, M., Raspaud, A.: Covering a graph by forests and a matching. arXiv:1007.0316v1 (2010)
Kim, S.-J., Kostochka, A.V., West, D.B., Wu, H., Zhu, X.: Decomposition of sparse graphs into forests and a graph with bounded degree (2010) (submitted)
Király, T., Lau, L.C., Singh, M.: Degree bounded matroids and submodular flows. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 259–272. Springer, Heidelberg (2008)
Montassier, M., Ossona de Mendez, P., Raspaud, A., Zhu, X.: Decomposing a graph into forests (2010) (manuscript)
Montassier, M., Pecher, A., Raspaud, A., West, D.B., Zhu, X.: Decomposition of sparse graphs, with application to game coloring number. Discrete Mathematics 310, 1520–1523 (2010)
Nash-Williams, C.S.J.A.: Decomposition of finite graphs into forests. J. London Math. Soc. 39(12) (1964)
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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
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