Preprocessing vertex-deletion problems: Characterizing graph properties by low-rank adjacencies

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Samenvatting

We consider the Π-free Deletion problem parameterized by the size of a vertex cover, for a range of graph properties Π. Given an input graph G, this problem asks whether there is a subset of at most k vertices whose removal ensures the resulting graph does not contain a graph from Π as induced subgraph. Many vertex-deletion problems such as Perfect Deletion, Wheel-free Deletion, and Interval Deletion fit into this framework. We introduce the concept of characterizing a graph property Π by low-rank adjacencies, and use it as the cornerstone of a general kernelization theorem for Π-Free Deletion parameterized by the size of a vertex cover. The resulting framework captures problems such as AT-Free Deletion, Wheel-free Deletion, and Interval Deletion. Moreover, our new framework shows that the vertex-deletion problem to perfect graphs has a polynomial kernel when parameterized by vertex cover, thereby resolving an open question by Fomin et al. [JCSS 2014]. Our main technical contribution shows how linear-algebraic dependence of suitably defined vectors over F2 implies graph-theoretic statements about the presence of forbidden induced subgraphs.

Originele taal-2Engels
Titel17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020
RedacteurenSusanne Albers
UitgeverijSchloss Dagstuhl - Leibniz-Zentrum für Informatik
ISBN van elektronische versie9783959771504
DOI's
StatusGepubliceerd - 1 jun 2020
Evenement17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020 - Torshavn, Faerøer
Duur: 22 jun 202024 jun 2020

Publicatie series

NaamLeibniz International Proceedings in Informatics, LIPIcs
Volume162
ISSN van geprinte versie1868-8969

Congres

Congres17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020
LandFaerøer
StadTorshavn
Periode22/06/2024/06/20

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