On the connectivity of configuration graphs
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Yuriy L. Pavlov
Abstract
We consider configuration graphs with vertex degrees being independent identically distributed random variables. The distribution of these variables satisfies only relatively weak constraints on the probabilities of large values of degrees. For the case when the number of vertices tends to infinity, the conditions are found under which the graph is asymptotically almost surely connected. We also give estimates of the rate of convergence to zero of the probability that the graph is not connected.
Note: Originally published in Diskretnaya Matematika (2019) 31, №2, 114–122 (in Russian).
Funding statement: Research was supported by the Federal budget for the fulfillment of the State assignment to the KarRC RAS (Institute of Applied Mathematical Research of Karelian Research Centre RAS)
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Articles in the same Issue
- Frontmatter
- Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem
- Pseudo orthogonal Latin squares
- Panchromatic colorings of random hypergraphs
- On the connectivity of configuration graphs
- Asymptotics with remainder term for moments of the total cycle number of random A-permutation
- On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
- Letter to the Editor
Articles in the same Issue
- Frontmatter
- Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem
- Pseudo orthogonal Latin squares
- Panchromatic colorings of random hypergraphs
- On the connectivity of configuration graphs
- Asymptotics with remainder term for moments of the total cycle number of random A-permutation
- On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
- Letter to the Editor
