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Enumerating Minimal Transversals of Hypergraphs without Small Holes

Authors Mamadou M. Kanté, Kaveh Khoshkhah, Mozhgan Pourmoradnasseri

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph enumeration
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Triangle-free Hypergraph
  • Minimal Transversal
  • Balanced Matrix
  • Minimal Dominating Set

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Abstract

We give a polynomial delay algorithm for enumerating the minimal transversals of hypergraphs without induced cycles of length 3 and 4. As a corollary, we can enumerate, with polynomial delay, the vertices of any polyhedron P(A,1)={x in R^n | Ax >= 1, x >= 0}, when A is a balanced matrix that does not contain as a submatrix the incidence matrix of a cycle of length 4. Other consequences are a polynomial delay algorithm for enumerating the minimal dominating sets of graphs of girth at least 9 and an incremental delay algorithm for enumerating all the minimal dominating sets of a bipartite graph without induced 6 and 8-cycles.

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Mamadou M. Kanté, Kaveh Khoshkhah, and Mozhgan Pourmoradnasseri. Enumerating Minimal Transversals of Hypergraphs without Small Holes. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.MFCS.2018.55

Author Details

Mamadou M. Kanté
  • Université Clermont Auvergne, LIMOS, CNRS , Aubiére, France
Kaveh Khoshkhah
  • Institute of Computer Science, University of Tartu , Tartu, Estonia
Mozhgan Pourmoradnasseri
  • Université Clermont Auvergne, LIMOS, CNRS , Aubiére, France

Funding

M. M. Kanté and M. Pourmoradnasseri are supported by the French Agency for Research under the GraphEN project ANR-15-CE40-0009.
  • Khoshkhah, Kaveh: Kaveh Khoshkhah was supported by the Estonian Research Council, ETAG (Eesti Teadusagentuur), through PUT Exploratory Grant #620.

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