1 Search Results for "Anand, Aditya"

Document

DOI: 10.4230/LIPIcs.IPEC.2021.1

A Polynomial Kernel for Deletion to Ptolemaic Graphs

Authors: Akanksha Agrawal, Aditya Anand, and Saket Saurabh

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract

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.

Cite as

Akanksha Agrawal, Aditya Anand, and Saket Saurabh. A Polynomial Kernel for Deletion to Ptolemaic Graphs. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{agrawal_et_al:LIPIcs.IPEC.2021.1,
  author =	{Agrawal, Akanksha and Anand, Aditya and Saurabh, Saket},
  title =	{{A Polynomial Kernel for Deletion to Ptolemaic Graphs}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{1:1--1:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.1},
  URN =		{urn:nbn:de:0030-drops-153840},
  doi =		{10.4230/LIPIcs.IPEC.2021.1},
  annote =	{Keywords: Ptolemaic Deletion, Kernelization, Parameterized Complexity, Gem-free chordal graphs}
}

Refine by Author
1 Agrawal, Akanksha
1 Anand, Aditya
1 Saurabh, Saket

Refine by Classification
1 Theory of computation → Parameterized complexity and exact algorithms

Refine by Keyword
1 Gem-free chordal graphs
1 Kernelization
1 Parameterized Complexity
1 Ptolemaic Deletion

Refine by Type
1 document

Refine by Publication Year
1 2021

1 Search Results for "Anand, Aditya"

A Polynomial Kernel for Deletion to Ptolemaic Graphs

Abstract

Cite as

Thanks for your feedback!

Could not send message