@techreport{TR-IC-10-23,
   number = {IC-10-23},
   author = {C. N. Campos and S. Dantas and C. P. de Mello},
   title = {Clique-colouring of some circulant graphs},
   month = {July},
   year = {2010},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 15 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       A  clique-colouring  of  a  graph  $G$  is  a  colouring of the
       vertices  of $G$ so that no maximal clique of size at least two
       is monochromatic. The clique-hypergraph, $\mathcal{H}(G)$, of a
       graph  $G$  has  $V(G)$  as its set of vertices and the maximal
       cliques  of  $G$  as  its  hyperedges.  A  vertex-colouring  of 
       $\mathcal{H}(G)$  is a clique-colouring of $G$. Determining the
       clique-chromatic  number, the least number of colours for which
       a   graph  $G$  admits  a  clique-colouring,  is  known  to  be 
       \emph{NP}-hard.  By  determining  some structural properties of
       powers of cycles, we establish that the clique-chromatic number
       of  these graphs is equal to two, except for odd cycles of size
       at  least  five, that need three colours. For odd-seq circulant
       graphs,  we  show that their clique-chromatic number is at most
       four,  and determine the cases when it is equal to two. Similar
       bounds  for  the  chromatic  number  of  these  graphs are also
       obtained.
  }
}