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A319492 Number of connected non-3-semi-transitively orientable graphs on n vertices. 0
0, 1, 25, 929, 54953, 4879508 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)