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On Balanced Graphs

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Abstract

Berge defined a hypergraph to be balanced if its incidence matrix is balanced. We consider this concept applied to graphs, and call a graph to be balanced when its clique matrix is balanced. Characterizations of balanced graphs by forbidden subgraphs and by clique subgraphs are proved in this work. Using properties of domination we define four subclasses of balanced graphs. Two of them are characterized by 0–1 matrices and can be recognized in polynomial time. Furthermore, we propose polynomial time combinatorial algorithms for the problems of stable set, clique-independent set and clique-transversal for one of these subclasses of balanced graphs. Finally, we analyse the behavior of balanced graphs and these four subclasses under the clique graph operator.

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Authors and Affiliations

  1. Dep. de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina

    Flavia Bonomo & Min Chih Lin

  2. Dep. de Ingeniería Industrial, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile

    Guillermo Durán

  3. Instituto de Matemática, NCE and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 2324, 20001-970, Rio de Janeiro, RJ, Brasil

    Jayme L Szwarcfiter

Authors
  1. Flavia Bonomo
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  2. Guillermo Durán
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  3. Min Chih Lin
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  4. Jayme L Szwarcfiter
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Correspondence to Flavia Bonomo.

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Received: April, 2004

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Bonomo, F., Durán, G., Lin, M. et al. On Balanced Graphs. Math. Program. 105, 233–250 (2006). https://doi.org/10.1007/s10107-005-0651-y

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