Polynomial kernels for edge modification problems towards block and strictly chordal graphs

We consider edge modification problems towards block and strictly chordal graphs, where one is given an undirected graph $G = (V,E)$ and an integer $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a block graph or a strictly chordal graph. The completion and...

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Vydáno v:	Discrete mathematics and theoretical computer science Ročník 27:2; číslo Discrete Algorithms
Hlavní autoři:	Dumas, Maël, Perez, Anthony, Rocton, Mathis, Todinca, Ioan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	DMTCS 01.05.2025 Discrete Mathematics & Theoretical Computer Science
Témata:	Computer Science computer science - computational complexity computer science - data structures and algorithms Data Structures and Algorithms
ISSN:	1365-8050, 1462-7264, 1365-8050
On-line přístup:	Získat plný text
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Popis
Shrnutí:	We consider edge modification problems towards block and strictly chordal graphs, where one is given an undirected graph $G = (V,E)$ and an integer $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a block graph or a strictly chordal graph. The completion and deletion variants of these problems are defined similarly by only allowing edge additions for the former and only edge deletions for the latter. Block graphs are a well-studied class of graphs and admit several characterizations, e.g. they are diamond-free chordal graphs. Strictly chordal graphs, also referred to as block duplicate graphs, are a natural generalization of block graphs where one can add true twins of cut-vertices. Strictly chordal graphs are exactly dart and gem-free chordal graphs. We prove the NP-completeness for most variants of these problems and provide $O(k^2)$ vertex-kernels for Block Graph Editing and Block Graph Deletion, $O(k^3)$ vertex-kernels for Strictly Chordal Completion and Strictly Chordal Deletion and a $O(k^4)$ vertex-kernel for Strictly Chordal Editing.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.12998