@techreport{TR-IC-09-35,
   number = {IC-09-35},
   author  =  {Sheila Morais de {Almeida} and Célia Picinin {de Mello}
                   and Aurora {Morgana}},
   title = {Edge-Coloring of Split Graphs},
   month = {September},
   year = {2009},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 11 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       The  {\em  Classification  Problem}  is the problem of deciding
       whether  a  simple graph has chromatic index equals to $\Delta$
       or  $\Delta+1$,  where  $\Delta$  is  the maximum degree of the
       graph.  It  is  known  that  to decide if a graph has chromatic
       index equals to $\Delta$ is NP-complete. A {\em split graph} is
       a  graph  whose vertex set admits a partition into a stable set
       and  a  clique. The chromatic indexes for some subsets of split
       graphs,  such  as  split  graphs  with  odd  maximum degree and
       split-indifference  graphs, are known. However, for the general
       class, the problem remains unsolved. In this paper we exhibit a
       new  subset  of split graphs with even maximum degree that have
       chromatic   index  equal  to  $\Delta$.  Moreover,  we  present 
       polynomial  time  algorithms to perform an edge-coloring and to
       recognize these graphs.
  }
}