Abstract
2 K 2 -free graphs do not contain the complement of the chordless cycle on four vertices ( 2 K 2 ) as induced subgraph. A triangulation H of a graph G is a chordal graph that is obtained by adding edges. If no proper subgraph of H is a triangulation of G , H is a minimal triangulation of G . We will show that the split graphs are exactly the minimal triangulations of 2 K 2 -free graphs. This result implies a characterisation of the set of minimal triangulations of a single 2 K 2 -free graph by special maximal independent sets. As an application, we will give a linear-time algorithm for computing the treewidth of co-chordal graphs.
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