A319492 Number of connected non-3-semi-transitively orientable graphs on n vertices.

0, 1, 25, 929, 54953, 4879508

Offset

5,3

Comments

A graph is k-semi-transitively orientable if it admits an acyclic orientation that avoids shortcuts of length k or less. The notion of a k-semi-transitive orientation refines that of a semi-transitive orientation, which is the case of k equal infinity. For n<9, the number of non-3-semi-transitively orientable graphs is precisely the number of non-semi-transitively orientable graphs, which in turn is the same as the number of non-word-representable graphs. For n=9, there are four 3-semi-transitively orientable graphs which are not semi-transitively orientable.

Links

Table of n, a(n) for n=5..10.

Ozgur Akgun, Ian P. Gent, Sergey Kitaev, Hans Zantema, Solving computational problems in the theory of word-representable graphs, arXiv:1808.01215 [math.CO], 2018.

Example

The wheel graph W_5 is the only connected graph on 6 vertices that is non-3-semi-transitively orientable.

Crossrefs

The first four terms are the same as the terms 5 - 8 in A290814.

Sequence in context: A218589 A264006 A218203 * A290814 A218230 A219060

Adjacent sequences: A319489 A319490 A319491 * A319493 A319494 A319495

Keyword

nonn,more

Author

Sergey Kitaev, Sep 20 2018

Status

approved