Reconfiguring Independent Sets on Interval Graphs

Briański, Marcin; Felsner, Stefan; Jędrzej, Hodor,; Micek, Piotr

doi:10.4230/lipics.mfcs.2021.23

Cited by 4 publications

(3 citation statements)

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“…However, they did not provide any estimation on its diameter. Motivated by this question, Briański et al [5] recently showed that the diameter of TS k (G) is O(kn 2 ).…”

Section: Discussionmentioning

confidence: 99%

“…In particular, the tractability/intractability of whether there is a path between two given nodes and several subsequent questions (e.g., if yes, whether a shortest one can be found efficiently; whether the statement holds for any pair of nodes; and so on) have been well-investigated for several graphs G. Readers are referred to [16, for a quick summary of the recent results. In particular, some structural properties regarding the connectivity and diameter of TS k (G) can be derived from many of these algorithmic results [11,12,4,7,9,3,5]. (See Appendix A.)…”

Section: Introductionmentioning

confidence: 99%

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On Reconfiguration Graphs of Independent Sets under Token Sliding

Avis¹,

Hoang²

2022

Preprint

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An independent set of a graph G is a vertex subset I such that there is no edge joining any two vertices in I. Imagine that a token is placed on each vertex of an independent set of G. The TS-(TS k -) reconfiguration graph of G takes all non-empty independent sets (of size k) as its nodes, where k is some given positive integer. Two nodes are adjacent if one can be obtained from the other by sliding a token on some vertex to one of its unoccupied neighbors. This paper focuses on the structure and realizability of these reconfiguration graphs. More precisely, we study two main questions for a given graph G: (1) Whether the TS k -reconfiguration graph of G belongs to some graph class G (including complete graphs, paths, cycles, complete bipartite graphs, and connected split graphs) and ( 2) If G satisfies some property P (including s-partitedness, planarity, Eulerianity, girth, and the clique's size), whether the corresponding TS-(TS k -) reconfiguration graph of G also satisfies P, and vice versa.

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“…However, they did not provide any estimation on its diameter. Motivated by this question, Briański et al [5] recently showed that the diameter of TS k (G) is O(kn 2 ).…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Reconfiguration Graphs of Independent Sets under Token Sliding

Avis¹,

Hoang²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Independent Set Reconfiguration is solvable in polynomial time on even-hole free graphs [12] and cographs [3,5], while it is NP-complete on bipartite graphs [13]. Token Sliding is solvable in polynomial time on cographs [12], bipartite permutation graphs [9], and interval graphs [4,7], while it is PSPACE-complete on split graphs [2] and bipartite graphs [13]. The result of [9] does not yield Theorem 2 since their polynomial-time algorithm may provide a non-shortest reconfiguration sequence on bipartite permutation graphs.…”

Section: Introductionmentioning

confidence: 99%

An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

et al. 2022

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In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for deciding whether there is a reconfiguration sequence between two longest increasing subsequences in a sequence. This implies that Independent Set Reconfiguration and Token Sliding are polynomial-time solvable on permutation graphs, provided that the input two independent sets are largest among all independent sets in the input graph. We also consider a special case, where the underlying permutation graph of an input sequence is bipartite. In this case, we give a polynomial-time algorithm for finding a shortest reconfiguration sequence (if it exists).

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On the Complexity of Distance-d Independent Set Reconfiguration

Hoang

2023

WALCOM: Algorithms and Computation

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Reconfiguring Independent Sets on Interval Graphs

Cited by 4 publications

References 0 publications

On Reconfiguration Graphs of Independent Sets under Token Sliding

On Reconfiguration Graphs of Independent Sets under Token Sliding

An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

On the Complexity of Distance-d Independent Set Reconfiguration

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