Logical properties of random graphs from small addable classes
We establish zero-one laws and convergence laws for monadic second-order logic (MSO) (and, a fortiori, first-order logic) on a number of interesting graph classes. In particular, we show that MSO obeys a zero-one law on the class of connected planar graphs, the class of connected graphs of tree-widt...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2019-07-01
|
| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/3780/pdf |
| Summary: | We establish zero-one laws and convergence laws for monadic second-order
logic (MSO) (and, a fortiori, first-order logic) on a number of interesting
graph classes. In particular, we show that MSO obeys a zero-one law on the
class of connected planar graphs, the class of connected graphs of tree-width
at most $k$ and the class of connected graphs excluding the $k$-clique as a
minor. In each of these cases, dropping the connectivity requirement leads to a
class where the zero-one law fails but a convergence law for MSO still holds. |
|---|---|
| ISSN: | 1860-5974 |