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A119414 Number of triangle-free graphs g on n nodes for which the chromatic number chi(g) equals r(g)=ceil((Delta(g)+1+omega(g))/2). 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 21, 826, 39889 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Here Delta(g)=maximum node degree of g and omega(g)=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: A012645 A220069 A028469 * A012819 A202810 A204196

Adjacent sequences:  A119411 A119412 A119413 * A119415 A119416 A119417

KEYWORD

nonn

AUTHOR

Keith Briggs (keith.briggs(AT)bt.com), Jul 26 2006

STATUS

approved

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Last modified August 24 06:49 EDT 2017. Contains 291052 sequences.