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math.CO2022
Minors, connectivity, and diameter in randomly perturbed sparse graphs
Elad Aigner-Horev, Dan Hefetz, Michael Krivelevich
Extremal properties of sparse graphs, randomly perturbed by the binomial random graph are considered. It is known that every -vertex graph contains a complete minor of order…
math.CO2022
Cycle lengths in randomly perturbed graphs
Elad Aigner-Horev, Dan Hefetz, Michael Krivelevich
Let be an -vertex graph, where for some . A result of Bohman, Frieze and Martin from 2003 asserts that if , then pertu…