Smaller kernels for 3-leaf power modifications problems

A graph G is a 3-leaf power if there is a tree T and a bijective mapping f from V(G) to the set of leaves of T such that (u,v)∈E(G) if and only if the distance in T between f(u) and f(v) is at most 3 for every distinct u,v∈V(G). In the 3-Leaf Power Vertex Deletion (resp., 3-Leaf Power Completion) pr...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1055; p. 115483
Main Author: Tsur, Dekel
Format: Journal Article
Language:English
Published: Elsevier B.V 09.11.2025
Subjects:
Graph algorithms
Kernelization
Parameterized complexity
Parameterized complexity
Graph algorithms
Kernelization
ISSN:0304-3975
Online Access:Get full text
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Summary:A graph G is a 3-leaf power if there is a tree T and a bijective mapping f from V(G) to the set of leaves of T such that (u,v)∈E(G) if and only if the distance in T between f(u) and f(v) is at most 3 for every distinct u,v∈V(G). In the 3-Leaf Power Vertex Deletion (resp., 3-Leaf Power Completion) problem the input is a graph G and an integer k, and the goal is to decide whether G can be transformed into a 3-leaf power graph by deleting at most k vertices (resp., adding at most k edges). In this paper we give a kernel for 3-Leaf Power Vertex Deletion with O(k6) vertices and a kernel for 3-Leaf Power Completion with O(k2) vertices. Our results improve the previous O(k14)-vertices kernel for 3-Leaf Power Vertex Deletion [Ahn et al., 2023 [3]] and the O(k3)-vertices kernel for 3-Leaf Power Completion [Bessy et al., 2010 [5]].
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115483