Ear-decompositions of matching-covered graphs

Abstract

We call a graphmatching-covered if every line belongs to a perfect matching. We study the technique of “ear-decompositions” of such graphs. We prove that a non-bipartite matching-covered graph containsK 4 orK 2K 3 (the triangular prism). Using this result, we give new characterizations of those graphs whose matching and covering numbers are equal. We apply these results to the theory of τ-critical graphs.

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Dedicated to Tibor Gallai on his seventieth birthday

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Lovász, L. Ear-decompositions of matching-covered graphs. Combinatorica 3, 105–117 (1983). https://doi.org/10.1007/BF02579346

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AMS subject classification (1980)

  • 05 C 99