Markov bases of binary graph models of \(K_{4}\)-minor free graphs

DOI10.1016/j.jcta.2009.07.007zbMath1215.05173arXiv0810.1979OpenAlexW2017867756WikidataQ57601432 ScholiaQ57601432MaRDI QIDQ986112

Daniel Král', Ondřej Pangrác, Serguei Norine

Publication date: 11 August 2010

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.1979

zbMATH Keywords

series-parallel graphsbinary graph modelMarkov baseMarkov width

Mathematics Subject Classification ID

Graph minors (05C83)

Related Items

Gorenstein cut polytopes ⋮ Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs ⋮ Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals ⋮ Retracts and algebraic properties of cut algebras ⋮ Cycle algebras and polytopes of matroids ⋮ Seminormality, canonical modules, and regularity of cut polytopes ⋮ Multigraded commutative algebra of graph decompositions ⋮ The $h^{*}$-polynomial of the cut polytope of $K_{2,m}$ in the lattice spanned by its vertices

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Toric geometry of cuts and splits
• A finiteness theorem for Markov bases of hierarchical models
• Markov bases of binary graph models
• Markov bases for decomposable graphical models
• Algebraic algorithms for sampling from conditional distributions
• Dense graphs with cycle neighborhoods
• Toric fiber products
• On the toric algebra of graphical models

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