### Basic Research Project J1-7051

Independence and Domination in Structured Graph Classes

Project Title: Independence and Domination in Structured Graph Classes.

PI: Martin Milanič.

Project Code: J1-7051.

Type of the Project: basic research project.

Funding Organization: Slovenian Research Agency (ARRS).

Research Field (ARRS): 1.01.00 - Natural Sciences and Mathematics / Mathematics.

Duration: 1. 1. 2016 - 31. 12. 2018.

Project Category: B.

Yearly Range: 0,94 FTE (1600 research hours).

Sicris profile of the project is avaliable here.

Research Organizations:

University of Primorska, Andrej Marušič Institute,

University of Ljubljana, Faculty of Education,

University of Ljubljana, Faculty of Mechanical EngineeringFakulteta za strojništvo.

Project Members:

Chiarelli Nina (ARRS code: 35452) |

Estelyi Istvan (ARRS code: 35520) |

Hartinger Tatiana Romina (ARRS code: 36761) |

Hujdurović Ademir (ARRS code: 32518) |

Kovacs Istvan (ARRS code: 25997) |

Kutnar Klavdija (ARRS code: 24997) |

Kuzman Boštjan (ARRS code: 23501) |

Malnič Aleksander (ARRS code: 02507) |

Marušič Dragan (ARRS code: 02887) |

Miklavič Štefko (ARRS code: 21656) |

Milanič Martin (PI) (ARRS code: 30211) |

Orel Marko (ARRS code: 25610) |

Pisanski Tomaž (ARRS code: 01941) |

Stevanović Dragan (ARRS code: 29820) |

Šparl Primož (ARRS code: 23341) |

Verret Gabriel (ARRS code: 28586) |

Žerovnik Janez (ARRS code: 03430) |

Abstract:

In the past decades, Graph Theory has arisen as one of the main areas of contemporary scientific research in mathematics. While its rapid development is partially due to increasing importance of technology and networks where it finds many applications, a number of original and valuable contributions by distinguished researchers established Graph Theory as a mature mathematical discipline. Over the years the Slovenian School of Graph Theory has been an essential part of the development of Graph Theory on the global level. Its international recognition has attained levels comparable to those reached by similar institutions from the technologically most developed countries around the world.

This project proposal is focused on structural and algorithmic aspects of Graph Theory and concentrates on a selection of classical and modern promising research areas at the intersection of Graph Theory with Theoretical Computer Science: the independent set problem in hereditary graph classes; the study of the price of connectivity for variants of independence and domination; the study of graph classes defined by cliques and independent sets, including CIS graphs and equistable graphs; the study of graph classes defined by variants of domination; computational complexity and algorithms for variants of domination. In addition to the above described topics, the project also includes research in other related areas of graph theory, including Algebraic Graph Theory.