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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| Published in: | Theoretical computer science Vol. 1055; p. 115483 |
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| Abstract | 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]]. |
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| AbstractList | 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]]. |
| ArticleNumber | 115483 |
| Author | Tsur, Dekel |
| Author_xml | – sequence: 1 givenname: Dekel orcidid: 0000-0001-9763-3784 surname: Tsur fullname: Tsur, Dekel email: dekelts@cs.bgu.ac.il organization: Department of computer science, Ben-Gurion University of the Negev, Israel |
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