Generating the maximum spanning trees of a weighted graph
Journal of Algorithms
A faster algorithm to recognize undirected path graphs
Discrete Applied Mathematics
Journal of Algorithms
Intersection graphs of concatenable subtrees of graphs
Discrete Applied Mathematics
Intersection graphs of Helly families of subtrees
Discrete Applied Mathematics
Acyclic hypergraph projections
Journal of Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Linear-Time Recognition of Circular-Arc Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Unicyclic Networks: Compatibility and Enumeration
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Journal of Computer and System Sciences
A simpler linear-time recognition of circular-arc graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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Consider a 0-1 matrix M(i,j) with columns C={c"1,c"2,...,c"m}, and rows R, or-equivalently-a hypergraph M(R,C) having M as its adjacency matrix (where R are the vertices and C are the hyperedges). Denote r"i={c"j|c"j@?C and M(i,j)=1}. We consider the following two problems: (a) Is there a graph H, with vertex set C, such that every vertex subgraph H(r"i) of H is a tree and the intersection of every two such trees is also a tree? (b) Is there a graph H, with vertex set C, such that every H(r"i) is a unicycle and the intersection of every two and every three unicycles is a tree? These questions occur in application areas such as database management systems and computational biology; e.g., in the latter they arise in the context of the analysis of biological networks, primarily for the purpose of data clustering. We describe algorithms to find such intersection representations of a matrix M (and equivalently of the hypergraph M), when they exist.