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arXiv · 2006.13684

Kernelization of Whitney Switches

Fedor V. Fomin·Petr A. Golovach
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Abstract

A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations called Whitney switches. In this paper we consider the quantitative question arising from Whitney's theorem: Given two 2-isomorphic graphs, can we transform one into another by applying at most k Whitney switches? This problem is already NP-complete for cycles, and we investigate its parameterized complexity. We show that the problem admits a kernel of size O(k), and thus, is fixed-parameter tractable when parameterized by k.

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Fedor V. Fomin, Petr A. Golovach. 2020-06-24. Kernelization of Whitney Switches. https://arxiv.org/abs/2006.13684

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