Section: New Results

Readability of overlap graphs

We report further progress on the study of a theoretical parameter of graph named readability [8]. This work concerns graph theory mainly. The readability parameter measures the minimal length of strings that would be needed in order to label a graph such that it is an overlap graph over a set of strings of that length. So far, recent works on readability have not elucidated many aspects related to this parameter: the complexity of computing it is open, and it is not even known whether the corresponding decision problem is in NP. The only upper bound known for this parameter is exponential. This work focuses on certain graph families: bipartite chain graphs, grids, induced subgraphs of grids, and provides a characterization of bipartite graphs of readability 2.