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On the Galois Lattice of Bipartite Distance Hereditary Graphs

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

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Abstract

We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a Bipartite Distance Hereditary graph. We show that the lattice can be realized as the containment relation among directed paths in an arborescence. Moreover, a compact encoding of Bipartite Distance Hereditary graphs is proposed, that allows optimal time computation of neighborhood intersections and maximal bicliques.

The first author was partially supported by Italian MIUR project “La Matematica per la società e l’innovazione tecnologica–MATHTECH”. The second author was partially supported by Italian MIUR projects PRIN 2012C4E3KT “AMANDA – Algorithmics for MAssive and Networked DAta” and “Sottografi fault resilient e algoritmi per modelli di calcolo con memory faults”.

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Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo M. Picone, CNR, via dei Taurini 19, 00185, Rome, Italy

    Nicola Apollonio

  2. Dipartimento di Ingegneria dell’Impresa, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Rome, Italy

    Massimiliano Caramia

  3. Dipartimento di Scienze Statistiche, Sapienza Università di Roma, piazzale Aldo Moro 5, 00185, Rome, Italy

    Paolo Giulio Franciosa

Authors
  1. Nicola Apollonio
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  2. Massimiliano Caramia
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  3. Paolo Giulio Franciosa
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Corresponding author

Correspondence to Paolo Giulio Franciosa .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Apollonio, N., Caramia, M., Franciosa, P.G. (2015). On the Galois Lattice of Bipartite Distance Hereditary Graphs. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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