Excluding a Bipartite Circle Graph from Line Graphs

Abstract

We prove that, for a fixed bipartite circle graph H, all line graphs with sufficiently large rank-width (or clique-width) must have a pivot-minor isomorphic to H. To prove this, we introduce graphic delta-matroids. Graphic delta-matroids are minors of delta-matroids of line graphs and they generalize graphic and cographic matroids. (c) 2008 Wiley Periodicals, Inc. J Graph Theory 60: 183 203, 2009