License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ISAAC.2018.31
URN: urn:nbn:de:0030-drops-99790
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Feng, Qilong ; Tan, Guanlan ; Zhu, Senmin ; Fu, Bin ; Wang, Jianxin

New Algorithms for Edge Induced König-Egerváry Subgraph Based on Gallai-Edmonds Decomposition

LIPIcs-ISAAC-2018-31.pdf (0.4 MB)


König-Egerváry graphs form an important graph class which has been studied extensively in graph theory. Much attention has also been paid on König-Egerváry subgraphs and König-Egerváry graph modification problems. In this paper, we focus on one König-Egerváry subgraph problem, called the Maximum Edge Induced König Subgraph problem. By exploiting the classical Gallai-Edmonds decomposition, we establish connections between minimum vertex cover, Gallai-Edmonds decomposition structure, maximum matching, maximum bisection, and König-Egerváry subgraph structure. We obtain a new structural property of König-Egerváry subgraph: every graph G=(V, E) has an edge induced König-Egerváry subgraph with at least 2|E|/3 edges. Based on the new structural property proposed, an approximation algorithm with ratio 10/7 for the Maximum Edge Induced König Subgraph problem is presented, improving the current best ratio of 5/3. To the best of our knowledge, this paper is the first one establishing the connection between Gallai-Edmonds decomposition and König-Egerváry graphs. Using 2|E|/3 as a lower bound, we define the Edge Induced König Subgraph above lower bound problem, and give a kernel of at most 30k edges for the problem.

BibTeX - Entry

  author =	{Qilong Feng and Guanlan Tan and Senmin Zhu and Bin Fu and Jianxin Wang},
  title =	{{New Algorithms for Edge Induced K{\"o}nig-Egerv{\'a}ry Subgraph Based on Gallai-Edmonds Decomposition}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{31:1--31:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-99790},
  doi =		{10.4230/LIPIcs.ISAAC.2018.31},
  annote =	{Keywords: K{\"o}nig-Egerv{\'a}ry graph, Gallai-Edmonds decomposition}

Keywords: König-Egerváry graph, Gallai-Edmonds decomposition
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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