Abstract
It is shown, that for each constant k ≥ 1, the following problems can be solved in O(n) time: given a graph G, determine whether G has k vertex disjoint cycles, determine whether G has k edge disjoint cycles, determine whether G has a feedback vertex set of size ≤ k. Also, every class \(\mathcal{G}\), that is closed under minor taking, or that is closed under immersion taking, and that does not contain the graph formed by taking the disjoint union of k copies of K 3, has an \(\mathcal{O}\)(n) membership test algorithm.
This work has been partially supported by the ESPRIT II Basic Research Actions Program of the EC, under contract No. 3075 (project ALCOM).
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Bodlaender, H.L. (1992). On disjoint cycles. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_24
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DOI: https://doi.org/10.1007/3-540-55121-2_24
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