Reconfiguring Independent Sets on Interval Graphs
We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size k are reconfigurable in an n-vertex interval graph, then there is a reconfiguration sequence of length 𝒪(k⋅ n²). We also provide a construction in which the shortest reconfiguration sequence is of length Ω(k²⋅ n).
As a counterpart to these results, we also establish that Independent Set Reconfiguration is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.
reconfiguration
independent sets
interval graphs
Mathematics of computing~Graph theory
23:1-23:14
Regular Paper
M. Briański, J. Hodor, P. Micek are partially supported by a Polish National Science Center grant (BEETHOVEN; UMO-2018/31/G/ST1/03718).
Marcin
Briański
Marcin Briański
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Stefan
Felsner
Stefan Felsner
Institut für Mathematik, Technische Universität Berlin, Germany
http://page.math.tu-berlin.de/~felsner/
Jędrzej
Hodor
Jędrzej Hodor
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Piotr
Micek
Piotr Micek
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
http://page.math.tu-berlin.de/~micek/
10.4230/LIPIcs.MFCS.2021.23
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Marcin Briański, Stefan Felsner, Jędrzej Hodor, and Piotr Micek
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