## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger, D. Steurer and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, March 31, 2022, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Joost Jorritsma (Eindhoven University of Technology )

## Distance evolutions in growing preferential attachment graphs

In this talk we will study the evolution of the graph distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with parameters such that the asymptotic degree distribution has infinite second moment. First, we grow the graph until it contains $t$ vertices, then we sample $u_t, v_t$ uniformly at random from the largest component and study the evolution of the graph distance as the surrounding graph grows. This yields a stochastic process in $t'\ge t$ that we call the distance evolution. We identify a function $f(t,t')$ such that there exists a tight strip around this function that the distance evolution never leaves with high probability as $t$ tends to infinity. If time permits, we will also consider the generalization of graph distance to weighted distance, in which every edge is equipped with an independent copy of a non-negative random variable $L$. Based on joint work with Julia Komjathy.

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