Abstract
For a simple graph G, let ρ(G)=1+[max δ(G′)/2], where the maximum is taken over all induced subgraphs G′ and δ(G′) is the minimum degree of G′. It is known that the vertex set of G can be partitioned into at most ρ(G) subsets each of which induces a forest. We give a sufficient condition under which an NC algorithm exists for finding such a partition. From this, we obtain NC algorithms for finding such a partition for K 5-free or K 3,3-free graphs (i.e., graphs without a K 5 or K 3,3 minor). These algorithms can be used to obtain efficient NC approximation algorithms of ratio 3 for many NP-hard maximum induced-subgraph problems on K 5-free or K 3,3-free graphs.
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© 1995 Springer-Verlag Berlin Heidelberg
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Chen, ZZ. (1995). NC algorithms for partitioning sparse graphs into induced forests with an application. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015449
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DOI: https://doi.org/10.1007/BFb0015449
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