@techreport{TR-IC-07-21,
  number = {IC-07-21},
  author = {Cândida Nunes da Silva and Cláudio L.~Lucchesi},
  title = {Flow-Critical Graphs},
  month = {June},
  year = {2007}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 16 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       In this paper we introduce the concept of k-flow-critical
       graphs. These are graphs that do not admit a k-flow but such
       that any smaller graph obtained from it by contraction of edges
       or of sets of vertices is k-flowable. Throughout this paper we
       will refer to k-flow-critical graphs simply as k-critical.
       \par
       Any minimum counterexample for Tutte's 3-Flow and 5-Flow
       Conjectures must be 3-critical and 5-critical,
       respectively. Thus, any progress towards establishing good
       characterizations of k-critical graphs can represent progress
       in the study of these conjectures. We present some interesting
       properties satisfied by k-critical graphs discovered recently.
  }
}