TY - GEN
T1 - A Polynomial Kernel for Deletion to the Scattered Class of Cliques and Trees
AU - Jacob, Ashwin
AU - Majumdar, Diptapriyo
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© Ashwin Jacob, Diptapriyo Majumdar, and Meirav Zehavi.
PY - 2024/12/4
Y1 - 2024/12/4
N2 - The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to scattered graph classes, where after deletion, each connected component of the graph should belong to at least one of the given graph classes. While fixed-parameter algorithms were given for a wide variety of problems, little progress has been made on the kernelization complexity of any of them. Here, we present the first non-trivial polynomial kernel for one such deletion problem, where, after deletion, each connected component should be a clique or a tree - that is, as dense as possible or as sparse as possible (while being connected). We develop a kernel of O(k5) vertices for the same.
AB - The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to scattered graph classes, where after deletion, each connected component of the graph should belong to at least one of the given graph classes. While fixed-parameter algorithms were given for a wide variety of problems, little progress has been made on the kernelization complexity of any of them. Here, we present the first non-trivial polynomial kernel for one such deletion problem, where, after deletion, each connected component should be a clique or a tree - that is, as dense as possible or as sparse as possible (while being connected). We develop a kernel of O(k5) vertices for the same.
KW - Cliques or Trees Vertex Deletion
KW - Kernelization
KW - New Expansion Lemma
KW - Parameterized Complexity
KW - Scattered Graph Classes
UR - http://www.scopus.com/inward/record.url?scp=85213059369&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2024.41
DO - 10.4230/LIPIcs.ISAAC.2024.41
M3 - Conference contribution
AN - SCOPUS:85213059369
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 35th International Symposium on Algorithms and Computation, ISAAC 2024
A2 - Mestre, Julian
A2 - Wirth, Anthony
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 35th International Symposium on Algorithms and Computation, ISAAC 2024
Y2 - 8 December 2024 through 11 December 2024
ER -