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- Martin Charles Golumbic, Haim Kaplan, Ron Shamir
- J. Algorithms
- 1995

A sandwich problem for a graph with respect to a graph property Π is a partially specified graph, i.e., only some of the edges and non-edges are given, and the question to be answered is, can this graph be completed to a graph which has the property Π? The graph sandwich problem was investigated for a large number of families of graphs in a 1995 paper by… (More)

- Martin Charles Golumbic, Ron Shamir
- J. ACM
- 1993

Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially speci ed. This work uni es notions of interval algebras in arti cial intelligence with those of interval orders and interval graphs in… (More)

- Martin Charles Golumbic, Peter L. Hammer, +18 authors Gerhard Jäger
- Annals of Mathematics and Artificial Intelligence
- 2004

Annals of Mathematics and Artificial Intelligence presents a range of topics of concern to scholars applying quantitative, combinatorial, logical, algebraic and algorithmic methods to diverse areas of Artificial Intelligence, from decision support, automated deduction, and reasoning, to knowledge-based systems, machine learning, computer vision, robotics… (More)

- Paul W. Goldberg, Martin Charles Golumbic, Haim Kaplan, Ron Shamir
- Journal of Computational Biology
- 1995

Physical mapping is a central problem in molecular biology and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NP-complete decision problems: Colored unit interval graph completion, the… (More)

- Martin Charles Golumbic, Udi Rotics
- Int. J. Found. Comput. Sci.
- 2000

- Martin Charles Golumbic, Robert E. Jamison
- J. Comb. Theory, Ser. B
- 1985

We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k 1) intersection graph k(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members ofP share k edges in T . An undirected graphG is… (More)

- Martin Charles Golumbic, Clyde L. Monma, William T. Trotter
- Discrete Applied Mathematics
- 1984

Tolerance graphs arise from the intersection of intervals with varying tolerances in a way that generalizes both interval graphs and permutation graphs. In this paper we prove that every tolerance graph is perfect by demonstrating that its complement is perfectly orderable. We show that a tolerance graph cannot contain a chordless cycle of length greater… (More)

- Martin Charles Golumbic, Tirza Hirst, Moshe Lewenstein
- Algorithmica
- 2001

A matching in a graph is a set of edges no two of which share a common vertex. In this paper we introduce a new, specialized type of matching which we call uniquely restricted matchings, originally motivated by the problem of determining a lower bound on the rank of a matrix having a specified zero/ non-zero pattern. A uniquely restricted matching is… (More)

- Martin Charles Golumbic, Robert E. Jamison
- Discrete Mathematics
- 1985

- Martin Charles Golumbic, Doron Rotem, Jorge Urrutia
- Discrete Mathematics
- 1983

A function diagram (f-diagram) D consists of the family of curves {i, . . . , ii} obtained from n continuous functions fi : [O, 1] -B R (1 G i d n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement 0 is a comparability graph. An f-diagram generalizes the notion cf a… (More)