|
Search: id:A119414
|
|
|
| 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
1
|
|
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 21, 826, 39889
(list; graph; listen)
|
|
|
OFFSET
|
1,12
|
|
|
COMMENT
|
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).
|
|
CROSSREFS
|
Sequence in context: A012850 A012645 A028469 this_sequence A012819 A041843 A041840
Adjacent sequences: A119411 A119412 A119413 this_sequence A119415 A119416 A119417
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Keith Briggs (keith.briggs(AT)bt.com), Jul 26 2006
|
|
|
Search completed in 0.002 seconds
|
