Algorithms for subgraph complementation to some classes of graphs

Antony, D and Pal, S and Sandeep, RB (2025) Algorithms for subgraph complementation to some classes of graphs. In: Information Processing Letters, 188 .

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Abstract

For a class G of graphs, the objective of SUBGRAPH COMPLEMENTATION TO G is to find whether there exists a subset S of vertices of the input graph G such that modifying G by complementing the subgraph induced by S results in a graph in G. We obtain a polynomial-time algorithm for the problem when G is the class of graphs with minimum degree at least k, for a constant k, answering an open problem by Fomin et al. (Algorithmica, 2020). When G is the class of graphs without any induced copies of the star graph on t+1 vertices (for any constant t�3) and diamond, we obtain a polynomial-time algorithm for the problem. This is in contrast with a result by Antony et al. (Algorithmica, 2022) that the problem is NP-complete and cannot be solved in subexponential-time (assuming the Exponential Time Hypothesis) when G is the class of graphs without any induced copies of the star graph on t+1 vertices, for every constant t�5. © 2024 Elsevier B.V.

Item Type:	Journal Article
Publication:	Information Processing Letters
Publisher:	Elsevier B.V.
Additional Information:	The copyright for this article belongs to the authors.
Keywords:	Graph theory; Polynomial approximation, Class G; Complementation; Graph G; Input graphs; Kernelization; Minimum degree; Polynomial-time algorithms; Star graphs; Subgraph complementation; Subgraphs, Graphic methods
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	09 Sep 2024 10:15
Last Modified:	09 Sep 2024 10:15
URI:	http://eprints.iisc.ac.in/id/eprint/85953

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