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The Complexity of Finding S-Factors in Regular Graphs

Authors Sanjana Kolisetty, Linh Le, Ilya Volkovich, Mihalis Yannakakis

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Author Details

Sanjana Kolisetty
  • Departments of Mathematics and EECS, CSE Division, University of Michigan, Ann Arbor, MI, USA
Linh Le
  • Departments of Mathematics and EECS, CSE Division, University of Michigan, Ann Arbor, MI, USA
Ilya Volkovich
  • Department of EECS, CSE Division, University of Michigan, Ann Arbor, MI, USA
Mihalis Yannakakis
  • Department of Computer Science, Columbia University, New York, NY, USA


The authors would like to thank the anonymous referees for their detailed comments and suggestions on the previous version of the paper.

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Sanjana Kolisetty, Linh Le, Ilya Volkovich, and Mihalis Yannakakis. The Complexity of Finding S-Factors in Regular Graphs. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 21:1-21:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


A graph G has an S-factor if there exists a spanning subgraph F of G such that for all v in V: deg_F(v) in S. The simplest example of such factor is a 1-factor, which corresponds to a perfect matching in a graph. In this paper we study the computational complexity of finding S-factors in regular graphs. Our techniques combine some classical as well as recent tools from graph theory.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Matchings and factors
  • Theory of computation → Problems, reductions and completeness
  • constraint satisfaction problem
  • Dichotomy theorem
  • Graph Factors
  • Regular Graphs


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