A119414 Number of triangle-free graphs g on n nodes for which the chromatic number chi(g) equals r(g) = ceiling((Delta(g) + 1 + omega(g))/2).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 21, 826, 39889

Offset

1,12

Comments

Here Delta(g) is the maximum node degree of g and omega(g) is the clique number of g (=2 for triangle-free graphs). r(g) is conjectured by Reed to be an upper bound for chi(g) for all graphs.

The sequence is of interest as a measure of how frequently the bound is attained. For example, for n=14 there are 467871369 triangle-free graphs.

References

B. Reed, omega, Delta and chi, J Graph Theory 27, 177-212 (1998).

Links

Table of n, a(n) for n=1..14.

Crossrefs

Sequence in context: A028469 A295845 A366301 * A012819 A297718 A296384

Adjacent sequences: A119411 A119412 A119413 * A119415 A119416 A119417

Keyword

nonn

Author

Keith Briggs, Jul 26 2006

Status

approved