# Algorithmic aspects of intersection graphs and representation hypergraphs

@article{Golumbic1988AlgorithmicAO, title={Algorithmic aspects of intersection graphs and representation hypergraphs}, author={Martin Charles Golumbic}, journal={Graphs and Combinatorics}, year={1988}, volume={4}, pages={307-321} }

Let ℛ be a family of sets. The intersection graph of ℛ is obtained by representing each set in ℛ by a vertex and connecting two vertices by an edge if and only if their corresponding sets intersect. Of primary interest are those classes of intersection graphs of families of sets having some specific topological or other structure. The “grandfather” of all intersection graphs is the class of interval graphs, that is, the intersection graphs of intervals on a line.The scope of research that has…

## 17 Citations

### Graph clustering: complexity, sequential and parallel algorithms

- Mathematics
- 1995

It is proved that the problem of partitioning the vertices of a graph into subgraphs of bounded diameter is NP-complete on bipartite and chordal graphs and an e cient parallel algorithm is presented for solving this problem on a class of unit interval graphs.

### Approximation Algorithms for Intersection Graphs

- MathematicsAlgorithmica
- 2012

The similarity to chordal graphs is used to construct simple polynomial-time approximation algorithms with constant approximation ratio for many NP-hard problems, when restricted to graphs for which at least one of the three complexity parameters is bounded by a constant.

### Complexity and Algorithms for Graph and Hypergraph Sandwich Problems

- Mathematics, Computer ScienceGraphs Comb.
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The NP-completeness of the Interval HSP and the Circular-arc HSP is proved and the k-tree graph sandwich problem is studied and the general problem is shown to be NP-complete and the fixed k version is given a polynomial algorithm.

### Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets

- MathematicsJournal of Automated Reasoning
- 2012

It is proved formally that every connected claw-free graph admits (1) a near-perfect matching, (2) Hamiltonian cycles in its square.

### Be sparse! Be dense! Be robust!: elements of parameterized algorithmics

- Mathematics, Computer Science
- 2017

It is shown that SUBSET INTERCONNECTION DESIGN admits a fixed-parameter algorithm with respect to the number of hyperedges in the input hypergraph, and Motivated by applications in network design, this thesis studies SUBSet INTER CONNECTIONDESIGN, where the support shall contain at most an integer f and the solution graphs shall have a certain property specific to the problem.

### Dually Chordal Graphs

- MathematicsSIAM J. Discret. Math.
- 1998

Recently in several papers ([10],[22],[42]) independently graphs with maximum neighbourhood orderings were characterized and turned out to be algorithmically useful.

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