Ear-decompositions of matching-covered graphs

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We call a graph matching-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 contains K 4 or K 2⊕K 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.

Original languageEnglish
Pages (from-to)105-117
Number of pages13
JournalCombinatorica
Volume3
Issue number1
DOIs
Publication statusPublished - Mar 1983

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Graph Matching
Prisms
Decomposition
Decompose
Graph Covering
Triangular prism
Matching number
Covering number
Critical Graph
Perfect Matching
Line
Graph in graph theory

Keywords

  • AMS subject classification (1980): 05C99

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)
  • Computational Mathematics

Cite this

Ear-decompositions of matching-covered graphs. / Lovász, L.

In: Combinatorica, Vol. 3, No. 1, 03.1983, p. 105-117.

Research output: Contribution to journalArticle

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