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Matching-perfect and cover-perfect graphs

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Abstract

It is shown that a graphG has all matchings of equal size if and only if for every matching setλ inG, G\V(λ) does not contain a maximal open path of odd length greater than one, which is not contained in a cycle. (V(λ) denotes the set of vertices incident with some edge ofλ.) Subsequently edge-coverings of graphs are discussed. A characterization is supplied for graphs all whose minimal covers have equal size.

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References

  1. B. Grünbaum,Matchings in polytopal graphs, Networks (to appear).

  2. M. Lewin,A note on line coverings of graphs, Discrete Math.5 (1973), 283–285.

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Authors and Affiliations

  1. Department of Mathematics, The Technion—Israel Institute of Technology, Haifa, Israel

    Mordechai Lewin

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  1. Mordechai Lewin
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Lewin, M. Matching-perfect and cover-perfect graphs. Israel J. Math. 18, 345–347 (1974). https://doi.org/10.1007/BF02760842

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  • DOI: https://doi.org/10.1007/BF02760842

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