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doi:10.1016/S0020-0190(98)00028-3 
Copyright © 1998 Published by Elsevier Science B.V.
Intersection graphs of k-acyclic families of subtrees and relational database query processing
Received 10 December 1996;
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Abstract
A graph G is called k-neighborhood chordal if for every vertex set A, such that ¦A¦ 
k and G(A) connected, the graph 
v ε A G(Γv) is chordal. A family of subtrees of a graph is called k-acyclic if the union of any k subtrees is acyclic. A graph is 1-neighborhood chordal iff it is an intersection graph of a Helly 2-acyclic family of subtrees (Gavril, 1987). In the present paper we prove that a graph is an intersection graph of a k-macyclic, k 
3, family of subtrees of a graph iff it is (k − 1)-neighborhood chordal iff it is 1-neighborhood chordal and when k 4 it contains no holes with k or less vertices. We present a polynomial time algorithm to find the biggest such k and to construct the corresponding family of subtrees. As an application, we use (k − 1)-neighborhood chordal graphs for a relaxation of the acyclicity requirement on versions of universal relations in relational databases, which still allows queries with at most k − 1 attributes to be answered by an efficient SPJ program.
Author Keywords: Algorithms; Intersection graph of subtrees; 2-acyclic family of subtrees; Neighborhood chordal graph; Acyclic relational database
