Abstract
Seidel’s switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non-adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching-equivalent if one can be made isomorphic to the other one by a sequence of switches.
Jelínková et al. [DMTCS 13, no. 2, 2011] presented a proof that it is NP-complete to decide if the input graph can be switched to contain at most a given number of edges. There turns out to be a flaw in their proof. We present a correct proof.
Furthermore, we prove that the problem remains NP-complete even when restricted to graphs whose density is bounded from above by an arbitrary fixed constant. This partially answers a question of Matoušek and Wagner [Discrete Comput. Geom. 52, no. 1, 2014].
V. Jelínek and J. Kratochvíl—Supported by CE-ITI project GACR P202/12/G061.
E. Jelínková—Supported by the grant SVV-2016-260332.
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Jelínek, V., Jelínková, E., Kratochvíl, J. (2016). On the Hardness of Switching to a Small Number of Edges. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_13
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DOI: https://doi.org/10.1007/978-3-319-42634-1_13
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