On the Hardness of Switching to a Small Number of Edges

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333131" target="_blank" >RIV/00216208:11320/16:10333131 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-42634-1_13" target="_blank" >http://dx.doi.org/10.1007/978-3-319-42634-1_13</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-42634-1_13" target="_blank" >10.1007/978-3-319-42634-1_13</a>

Result language
angličtina
Original language name
On the Hardness of Switching to a Small Number of Edges
Original language 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 one by a sequence of switches. Jelinkova 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 Matou. sek and Wagner [Discrete Comput. Geom. 52, no. 1, 2014].
Czech name
—
Czech description
—

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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