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A119414
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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).
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0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 21, 826, 39889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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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.
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REFERENCES
| B. Reed, omega, Delta and chi, J Graph Theory 27, 177-212 (1998).
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CROSSREFS
| Sequence in context: A012850 A012645 A028469 * A012819 A202810 A204196
Adjacent sequences: A119411 A119412 A119413 * A119415 A119416 A119417
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KEYWORD
| nonn
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AUTHOR
| Keith Briggs (keith.briggs(AT)bt.com), Jul 26 2006
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