The Graph Sparsity Theory of Nešetřil and Ossona de Mendez is a highly active and rapidly developing topic in combinatorics and graph theory, with applications in many areas including algorithmic graph theory, complexity theory, and property testing. A recent focus of structural and algorithmic graph theory has been to extend the graph sparsity theory to dense graph classes. The proposed project aims at introducing novel ways and methods of addressing this goal. This will be done along the following two interconnected research lines:

• first, by advancing the recently emerging and fast developing theory of graph width and depth parameters through a general framework based on graph measures and an in-depth analysis of known and novel graph parameters;
• second, by developing a biparametric theory of hereditary graph classes in which some parameter is bounded by a function of another one, with the goal of identifying nontrivial structural and algorithmic implications. Our approach is expected to lead to an improved understanding of the boundaries of tractability for maximum independent set and several other practically relevant graph optimization problems. The successful candidate will be part of the Departments of Mathematics at UP FAMNIT and UP IAM and will work under the guidance of Prof. Martin Milanič.

Terms and conditions:

• The position is for two years.
• Applicants must possess (or expect to obtain shortly) a PhD in Mathematics, Computer Science, or a related area, and show evidence of excellence in discrete mathematics or theoretical computer science. Candidates who completed their PhD recently or will do so by next September are encouraged to apply.
• Relevant expertise in structural and algorithmic graph theory is required, including a solid knowledge of various aspects of graph theory, algorithms, and computational complexity theory.
• The position will require teaching at most two courses per year in Mathematics or Computer Science programs at UP FAMNIT (depending on the candidate's background and expertise).
• The postdoctoral researcher will have access to a certain amount of funding for travel, conferences, and visitors.
• The compensation is set according to the academic title by Slovenian law governing higher education and is expected to be about 1680 EUR / month after tax, which can increase to about 1780 EUR / month after the first 6 months (if the tax residency status is obtained).

Deadline and application process:

Applications will be assessed on a rolling basis until the position is filled, beginning April 15, 2024. The starting date is flexible, but preferably not later than October 2024. To apply, please send the following documents in electronic form to razpisi@famnit.upr.si with the subject line "University of Primorska Postdoc 2024" in the Subject field:

• Curriculum Vitae,
• Publication List,
• Research Statement,
• Copies of at most three recent papers or preprints,
• Names and e-mail addresses of two or three persons who can be contacted for reference (and who have agreed to be contacted).

Informal inquiries may be directed by email to Martin Milanič (martin.milanic@upr.si).