**Abstract:** |
Let denote a circle of circumference . The circular
consecutive choosability of a graph is the least
real number such that for any , if each vertex
is assigned a closed interval of length on ,
then there is a circular -colouring of such that . We investigate, for a graph, the relations between its
circular consecutive choosability and choosibility. It is proved
that for any positive integer , if a graph is -choosable,
then ; moreover, the bound is sharp for . For , it is proved that if is -choosable then
, while the equality holds if and only if
contains a cycle. In addition, we prove that there exist circular
consecutive -choosable graphs which are not -choosable. In
particular, it is shown that holds for all cycles and
for with . On the other hand, we prove that holds for many generalized theta graphs. |