On minimal forbidden subgraph characterizations of balanced graphs |
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| Authors: | Flavia Bonomo Guillermo Durán Martín D Safe Annegret K Wagler |
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| Institution: | 1. CONICET, Argentina;2. Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina;3. Departamento de Matemática and Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina;4. Departamento de Ingeniería Industrial, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile;5. Instituto de Ciencias, Universidad Nacional de General Sarmiento, Los Polvorines, Argentina;6. CNRS and LIMOS, UFR Sciences et Technologies, Université Blaise Pascal, Clermont-Ferrand, France |
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| Abstract: | 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 linear-time recognition algorithms for balanced graphs within the same three graph classes. |
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| Keywords: | Balanced graphs Bipartite graphs Hereditary clique-Helly graphs Line graphs Perfect graphs |
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