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math.CO2019
Increasing paths in countable graphs
Andrii Arman, Bradley Elliott, Vojtěch Rödl
In this paper we study variations of an old result by Müller, Reiterman, and the last author stating that a countable graph has a subgraph with infinite degrees if and only if in a…
math.CO2019
Fast uniform generation of random graphs with given degree sequences
Andrii Arman, Pu Gao, Nicholas Wormald
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that , where is the maximal degree and is th…