Eva Jelinkova ; Ondrej Suchy ; Petr Hlineny ; Jan Kratochvil - Parameterized Problems Related to Seidel's Switching

dmtcs:542 - Discrete Mathematics & Theoretical Computer Science, May 10, 2011, Vol. 13 no. 2 - https://doi.org/10.46298/dmtcs.542
Parameterized Problems Related to Seidel's Switching

Authors: Eva Jelinkova ORCID-iD1; Ondrej Suchy 2; Petr Hlineny ORCID-iD3; Jan Kratochvil ORCID-iD4

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 by a sequence of switches. In this paper, we continue the study of computational complexity aspects of Seidel's switching, concentrating on Fixed Parameter Complexity. Among other results we show that switching to a graph with at most k edges, to a graph of maximum degree at most k, to a k-regular graph, or to a graph with minimum degree at least k are fixed parameter tractable problems, where k is the parameter. On the other hand, switching to a graph that contains a given fixed graph as an induced subgraph is W [1]-complete. We also show the NP-completeness of switching to a graph with a clique of linear size, and of switching to a graph with small number of edges. A consequence of the latter result is the NP-completeness of Maximum Likelihood Decoding of graph theoretic codes based on complete graphs.

Volume: Vol. 13 no. 2
Section: Graph and Algorithms
Published on: May 10, 2011
Accepted on: June 9, 2015
Submitted on: June 1, 2010
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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Source : ScholeXplorer IsRelatedTo DOI 10.1016/0166-218x(80)90038-4
  • 10.1016/0166-218x(80)90038-4
On deciding switching equivalence of graphs

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