On Hypergraph Acyclicity and Graph Chordality

Abstract Concepts of acyclicity in hypergraphs and chordality in graphs are related by showing that a hierarchy of well-studied classes of chordal graphs corresponds to the hierarchy of classes of acyclic hypergraphs studied in relational database theory (Fagin, 1983).

[1]  Nathan Goodman,et al.  Tree queries: a simple class of relational queries , 1982, TODS.

[2]  Giorgio Ausiello,et al.  Minimal Coverings of Acyclic Database Schemata , 1982, Advances in Data Base Theory.

[3]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[4]  Richard P. Anstee,et al.  Characterizations of Totally Balanced Matrices , 1984, J. Algorithms.

[5]  Mihalis Yannakakis,et al.  Testing the Universal Instance Assumption , 1980, Inf. Process. Lett..

[6]  Giorgio Ausiello,et al.  Chordality Properties on Graphs and Minimal Conceptual Connections in Semantic Data Models , 1986, J. Comput. Syst. Sci..

[7]  Marina Moscarini,et al.  Recognition Algorithms and Design Methodologies for Acyclic Database Schemes , 1986, Adv. Comput. Res..

[8]  I. Paz.  On the Traffic Handling Capability of Communication Networks Homogeneously Loaded , 1975, Networks.

[9]  Martin Farber,et al.  Characterizations of strongly chordal graphs , 1983, Discret. Math..

[10]  David Maier,et al.  Connections in Acyclic Hypergraphs , 1984, Theor. Comput. Sci..

[11]  Richard P. Anstee.  Hypergraphs with no special cycles , 1983, Comb..

[12]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[13]  Edward Howorka.  A characterization of ptolemaic graphs , 1981, J. Graph Theory.

[14]  Edward Howorka,et al.  On metric properties of certain clique graphs , 1979, J. Comb. Theory, Ser. B.

[15]  Hans-Jürgen Bandelt,et al.  Distance-hereditary graphs , 1986, J. Comb. Theory, Ser. B.

[16]  Ronald Fagin,et al.  Degrees of acyclicity for hypergraphs and relational database schemes , 1983, JACM.

[17]  Nathan Goodman,et al.  Syntactic Characterization of Tree Database Schemas , 1983, JACM.

[18]  Jenö Lehel.  A characterization of totally balanced hypergraphs , 1985, Discret. Math..

[19]  Zsolt Tuza,et al.  Hypergraphs without a large star , 1985, Discret. Math..

[20]  G. Chartrand,et al.  A Characterization of Certain Ptolemaic Graphs , 1965, Canadian Journal of Mathematics.

[21]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[22]  Martin Farber,et al.  Steiner trees, connected domination and strongly chordal graphs , 1985, Networks.

[23]  E. Howorka.  A CHARACTERIZATION OF DISTANCE-HEREDITARY GRAPHS , 1977 .