TY - GEN
T1 - A polynomial kernel for deletion to ptolemaic graphs
AU - Agrawal, Akanksha
AU - Anand, Aditya
AU - Saurabh, Saket
N1 - Publisher Copyright:
© Akanksha Agrawal, Aditya Anand, and Saket Saurabh; licensed under Creative Commons License CC-BY 4.0
PY - 2021/11/1
Y1 - 2021/11/1
N2 - For a family of graphs F, given a graph G and an integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in the family F. The F-Deletion problems for all non-trivial families F that satisfy the hereditary property on induced subgraphs are known to be NP-hard by a result of Yannakakis (STOC'78). Ptolemaic graphs are the graphs that satisfy the Ptolemy inequality, and they are the intersection of chordal graphs and distance-hereditary graphs. Equivalently, they form the set of graphs that do not contain any chordless cycles or a gem as an induced subgraph. (A gem is the graph on 5 vertices, where four vertices form an induced path, and the fifth vertex is adjacent to all the vertices of this induced path.) The Ptolemaic Deletion problem is the F-Deletion problem, where F is the family of Ptolemaic graphs. In this paper we study Ptolemaic Deletion from the viewpoint of Kernelization Complexity, and obtain a kernel with O(k6) vertices for the problem.
AB - For a family of graphs F, given a graph G and an integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in the family F. The F-Deletion problems for all non-trivial families F that satisfy the hereditary property on induced subgraphs are known to be NP-hard by a result of Yannakakis (STOC'78). Ptolemaic graphs are the graphs that satisfy the Ptolemy inequality, and they are the intersection of chordal graphs and distance-hereditary graphs. Equivalently, they form the set of graphs that do not contain any chordless cycles or a gem as an induced subgraph. (A gem is the graph on 5 vertices, where four vertices form an induced path, and the fifth vertex is adjacent to all the vertices of this induced path.) The Ptolemaic Deletion problem is the F-Deletion problem, where F is the family of Ptolemaic graphs. In this paper we study Ptolemaic Deletion from the viewpoint of Kernelization Complexity, and obtain a kernel with O(k6) vertices for the problem.
KW - Gem-free chordal graphs
KW - Kernelization
KW - Parameterized Complexity
KW - Ptolemaic Deletion
UR - http://www.scopus.com/inward/record.url?scp=85121151240&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.IPEC.2021.1
DO - 10.4230/LIPIcs.IPEC.2021.1
M3 - Conference contribution
AN - SCOPUS:85121151240
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 16th International Symposium on Parameterized and Exact Computation, IPEC 2021
A2 - Golovach, Petr A.
A2 - Zehavi, Meirav
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 16th International Symposium on Parameterized and Exact Computation, IPEC 2021
Y2 - 8 September 2021 through 10 September 2021
ER -