On minimal forbidden subgraph characterizations of balanced graphs

A graph is balanced if its clique-matrix contains no edge-vertex incidence matrix of an odd chordless cycle as a submatrix. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such characterization by minimal forbidden induced subgraphs. In this work, we provide minimal forbidden induced subgraph characterizations of balanced graphs restricted to graphs that belong to one of the following graph classes: complements of bipartite graphs, line graphs of multigraphs, and complements of line graphs of multigraphs. These characterizations lead to linearEmail addresses: [email protected] (Flavia Bonomo), [email protected] (Guillermo Durán), [email protected] (Mart́ın D. Safe), [email protected] (Annegret K. Wagler) Partially supported by ANPCyT PICT 2007-00518 and 2007-00533, and UBACyT Grants 20020100100980 and 20020090300094 (Argentina) Partially supported by FONDECyT Grant 1110797 and Millennium Science Institute “Complex Engineering Systems” (Chile), and ANPCyT PICT 2007-00518, UBACyT Grant 20020100100980, and CONICET PIP 112-200901-00178 (Argentina) Partially supported by ANPCyT PICT 2007-00518, UBACyT Grant 20020100100980, and CONICET PIP 112-200901-00178 (Argentina) Preprint submitted to Discrete Applied Mathematics April 7, 2013 time recognition algorithms for balanced graphs within the same three graph classes.