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Mexican International Conference on Artificial Intelligence

MICAI 2006: MICAI 2006: Advances in Artificial Intelligence pp 15–26Cite as

Properties of Markovian Subgraphs of a Decomposable Graph

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4293))

Abstract

We explore the properties of subgraphs (called Markovian subgraphs) of a decomposable graph under some conditions. For a decomposable graph \(\mathcal{G}\) and a collection γ of its Markovian subgraphs, we show that the set \(\chi(\mathcal{G})\) of the intersections of all the neighboring cliques of \(\mathcal{G}\) contains . We also show that \(\chi(\mathcal{G})=\cup_{g\in\gamma}\chi(g)\) holds for a certain type of \(\mathcal{G}\) which we call a maximal Markovian supergraph of γ. This graph-theoretic result is instrumental for combining knowledge structures that are given in undirected graphs.

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Author information

Authors and Affiliations

  1. Korea Advanced Institute of Science and Technology, Daejeon, 305-701, South Korea

    Sung-Ho Kim

Authors
  1. Sung-Ho Kim
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Editor information

Editors and Affiliations

  1. Center for Computing Research, National Polytechnic Institute, 07738, Mexico City, México

    Alexander Gelbukh

  2. Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Luis Enrique Erro No. 1, Sta. Ma. Tonanzintla, 72840, Puebla, México

    Carlos Alberto Reyes-Garcia

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© 2006 Springer-Verlag Berlin Heidelberg

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Kim, SH. (2006). Properties of Markovian Subgraphs of a Decomposable Graph. In: Gelbukh, A., Reyes-Garcia, C.A. (eds) MICAI 2006: Advances in Artificial Intelligence. MICAI 2006. Lecture Notes in Computer Science(), vol 4293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11925231_2

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  • DOI: https://doi.org/10.1007/11925231_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49026-5

  • Online ISBN: 978-3-540-49058-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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