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math.PR2022
Dynamic random graphs with vertex removal
Josep Díaz, Lyuben Lichev, Bas Lodewijks
We introduce and analyse a Dynamic Random Graph with Vertex Removal (DRGVR) defined as follows. At every step, with probability a new vertex is introduced, and with proba…
math.PR2022
On the first and second largest components in the percolated Random Geometric Graph
Lyuben Lichev, Bas Lodewijks, Dieter Mitsche +1
The percolated random geometric graph has vertex set given by a Poisson Point Process in the square , and every pair of vertices at distance at most 1 i…
math.PR2022
On joint properties of vertices with a given degree or label in the random recursive tree
Bas Lodewijks
In this paper, we study the joint behaviour of the degree, depth and label of and graph distance between high-degree vertices in the random recursive tree. We generalise the result…