@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.
}
}