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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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
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