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@article{950106,
author = {Hliněný, Petr and Jelínková, Eva and Kratochvíl, Jan and Suchý, Ondřej},
article_location = {France},
article_number = {2},
keywords = {graph; Seidel switching},
language = {eng},
issn = {1365-8050},
journal = {Discrete Mathematics & Theoretical Computer Science},
title = {Parameterized Problems Related to Seidel's Switching},
url = {http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/1531},
volume = {13},
year = {2011}
}
TY - JOUR
ID - 950106
AU - Hliněný, Petr - Jelínková, Eva - Kratochvíl, Jan - Suchý, Ondřej
PY - 2011
TI - Parameterized Problems Related to Seidel's Switching
JF - Discrete Mathematics & Theoretical Computer Science
VL - 13
IS - 2
SP - 19-42
EP - 19-42
PB - DMTCS
SN - 13658050
KW - graph
KW - Seidel switching
UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/1531
N2 - 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.
ER -
HLINĚNÝ, Petr, Eva JELÍNKOVÁ, Jan KRATOCHVÍL a Ondřej SUCHÝ. Parameterized Problems Related to Seidel's Switching. \textit{Discrete Mathematics \&{} Theoretical Computer Science}. France: DMTCS, 2011, roč.~13, č.~2, s.~19-42. ISSN~1365-8050.
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