The chromatic polynomial of a graph
,
denoted by
, is equal to the
number of proper
-colorings
of
for
each
.
In 1990, Kostochka and Sidorenko introduced the list color function of graph
, denoted
by
,
which is a list analogue of the chromatic polynomial. The
list color function threshold of
, denoted
by
, is the
smallest
such
that
and
whenever
. It is known that
for every graph
,
is finite, and a recent paper of Kaul et al. suggests that complete
bipartite graphs may be the key to understanding the extremal behavior
of
.
We develop tools for bounding the list color function threshold
of complete bipartite graphs from above. We show that, for any
,
. Interestingly,
our proof makes use of classical results such as Rolle’s theorem and Descartes’ rule of signs.
PDF Access Denied
We have not been able to recognize your IP address
18.219.103.183
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.