Most Graphs are Knotted
| Autor: | Kazuhiro Ichihara, Thomas W. Mattman |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Random graph
Algebra and Number Theory Computer Science::Information Retrieval Apex graph Primary 05C10 Secondary 57M15 05C35 Astrophysics::Instrumentation and Methods for Astrophysics Geometric Topology (math.GT) Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Mathematics::Geometric Topology Graph Combinatorics Mathematics - Geometric Topology FOS: Mathematics Computer Science::General Literature Mathematics |
| Popis: | We present four models for a random graph and show that, in each case, the probability that a graph is intrinsically knotted goes to one as the number of vertices increases. We also argue that, for $k \geq 18$, most graphs of order $k$ are intrinsically knotted and, for $k \geq 2n+9$, most of order $k$ are not $n$-apex. We observe that $p(n) = 1/n$ is the threshold for intrinsic knotting and linking in Gilbert's model. 5 pages |
| Databáze: | OpenAIRE |
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