### Abstract

We introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph D, an injective overlap labeling assigns a unique string to each vertex such that there is an arc from x to y if and only if x properly overlaps y. The readability of D is the minimum string length for which an injective overlap labeling exists. In applications that utilize overlap digraphs (e.g., in bioinformatics), readability reflects the length of the strings from which the overlap digraph is constructed. We study the asymptotic behaviour of readability by casting it in purely graph theoretic terms (without any reference to strings). We prove upper and lower bounds on readability for certain graph families and general graphs.

Original language | English (US) |
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Title of host publication | Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings |

Editors | Ugo Vaccaro, Ely Porat, Ferdinando Cicalese |

Publisher | Springer Verlag |

Pages | 124-137 |

Number of pages | 14 |

ISBN (Print) | 9783319199283 |

DOIs | |

State | Published - Jan 1 2015 |

Event | 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy Duration: Jun 29 2015 → Jul 1 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9133 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 |
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Country | Italy |

City | Ischia Island |

Period | 6/29/15 → 7/1/15 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings*(pp. 124-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_11