Parameterized Problems Related to Seidel's Switching
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Discrete Mathematics & Theoretical Computer Science |
| MU Faculty or unit | |
| Citation | |
| Web | paper |
| Field | General mathematics |
| Keywords | graph; Seidel switching |
| Description | 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. |
| Related projects: |