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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, 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).
CROSSREFS
Sequence in context: A028469 A295845 A366301 * A012819 A297718 A296384
KEYWORD
nonn
AUTHOR
Keith Briggs, Jul 26 2006
STATUS
approved