University of Groningen
Perfect matchings, Hamilton cycles, degree distribution and local clustering in Hyperbolic
Random Graphs
Schepers, Markus
DOI:
10.33612/diss.124993623
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Publication date: 2020
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Schepers, M. (2020). Perfect matchings, Hamilton cycles, degree distribution and local clustering in Hyperbolic Random Graphs. University of Groningen. https://doi.org/10.33612/diss.124993623
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Stellingen
Markus Schepers February 28, 2020
1. For all α 12, and all sufficiently small positive ν, the KPKVB hyperbolic random graphs do not have perfect matchings or Hamilton cycles asymptotically almost surely.
2. For all α 12, and all sufficiently large positive ν, the KPKVB hyperbolic random graphs have Hamilton cycles and (near) perfect matchings asymptotically almost surely.
3. For α ¡ 12, the degree distribution of the KPKVB hyperbolic random graphs follows a power-law with exponent 2α 1.
4. For α¡ 12 and all positive ν, the local clustering coefficient converges to a positive closed-form expression.
5. For α¡ 12 and all positive ν, the local clustering function for fixed degree converges to a positive closed-form expression.
6. For 12 α 34, the local clustering function scales like k24α, for α 34, it scales like log kk and for α¡ 34, it scales like 1k as the degree kÑ 8.
