## Abstract

Labeled graphs, in which edges are labeled by letters from some alphabet ∑, are extensively used to model many types of relations associated with actions, costs, owners, or other properties. Each path in a labeled graph induces a word in ∑∗- the one obtained by concatenating the letters along the edges in the path. Classical graph-theory problems give rise to new problems that take these words into account. We introduce and study the constrained Eulerian path problem. The input to the problem is a ∑-labeled graph G and a specification L ⊆ ∑∗. The goal is to find an Eulerian path in G that satisfies L. We consider several classes of the problem, defined by the classes of G and L. We focus on the case L is regular and show that while the problem is in general NP-complete, even for very simple graphs and specifications, there are classes that can be solved efficiently. Our results extend work on Eulerian paths with edge-order constraints. We also study the constrained Chinese postman problem, where edges have costs and the goal is to find a cheapest path that contains each edge at least once and satisfies the specification. Finally, we define and study the Eulerian language of a graph, namely the set of words along its Eulerian paths.

Original language | American English |
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Title of host publication | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |

Editors | Anca Muscholl, Piotr Faliszewski, Rolf Niedermeier |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770163 |

DOIs | |

State | Published - 1 Aug 2016 |

Event | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland Duration: 22 Aug 2016 → 26 Aug 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 58 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |
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Country/Territory | Poland |

City | Krakow |

Period | 22/08/16 → 26/08/16 |

### Bibliographical note

Publisher Copyright:© Orna Kupferman and Gal Vardi;.

## Keywords

- Eulerian Paths
- Regular Languages