The 
-chromatic
polynomial, introduced by Birkhoff and Lewis (1946) and termed the "
-chromial" by Bari (1974), is an alternate form of the
chromatic polynomial 
defined for graphs with chromatic
number 
by
 |
Its definition is motivated by the fact that 
for any graph with chromatic
number 
,
meaning dividing out the corresponding terms 
from 
provides a more compact representation than 
since 
has a smaller coefficients. When 
, 
is a polynomial of degree 
(instead of 
) for a graph with vertex count 
, and in the case where 
, it is a polynomial in 
of degree 
plus a term involving 
(Birkhoff and Lewis 1946).
