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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Properties of Markovian Subgraphs of a Decomposable Graph
verfasst von : Sung-Ho Kim
Erschienen in: MICAI 2006: Advances in Artificial Intelligence
Verlag: Springer Berlin Heidelberg
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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.