On the Random Minimal Edge-Disjoint Spanning Trees Problem

Student: Nikita Zvonkov

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 10

Year of Graduation: 2024

Finding minimal structures in weighted graphs can be hard. However, if the weights are random, this task can become way easier. In this paper, we examine the minimum union of k edge-disjoint trees in a complete graph with independent and identically distributed edge weights. The limit value of the weight of this structure (for a given distribution) was found for k=1,2. In this paper, we find the limit value of the weight for any k>2 and also prove a related result regarding the structure of sparse random graphs.

Full text (added May 19, 2024)

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