Properties of markovian subgraphs of a decomposable graph

Authors:
Sung-Ho Kim
Affiliations:
Korea Advanced Institute of Science and Technology, Daejeon, South Korea
Venue:
MICAI'06 Proceedings of the 5th Mexican international conference on Artificial Intelligence
Year:
2006

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Abstract

We explore the properties of subgraphs (called Markovian subgraphs) of a decomposable graph under some conditions. For a decomposable graph and a collection γ of its Markovian subgraphs, we show that the set of the intersections of all the neighboring cliques of contains . We also show that holds for a certain type of 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.