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On equivalence of Markov properties over undirected graphs

Part of: Stochastic processes Discrete mathematics in relation to computer science Graph theory

Published online by Cambridge University Press:  14 July 2016

F. Matúš
F. Matúš*
Affiliation:
Institute of Information Theory and Automation, Prague
*
∗Postal address: Institute of Information Theory and Automation, Czechoslovak Academy of Sciences, Pod vodárenskou véží 4, 182 08 Prague, Czechoslovakia.
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Abstract

The dependence of coincidence of the global, local and pairwise Markov properties on the underlying undirected graph is examined. The pairs of these properties are found to be equivalent for graphs with some small excluded subgraphs. Probabilistic representations of the corresponding conditional independence structures are discussed.

Keywords

MARKOV RANDOM FIELDSCONDITIONAL INDEPENDENCE

MSC classification

Primary: 68R10: Graph theory (including graph drawing)
Secondary: 05C80: Random graphs 60G60: Random fields
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 745 - 749
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

This research was supported partially by Internal Grant 27510 of Czechoslovak Academy of Sciences.

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