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On minimal strong blocks
Author(s) -
Grötschel Martin
Publication year - 1979
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190030303
Subject(s) - mathematics , combinatorics , bounded function , decomposition , discrete mathematics , biology , ecology , mathematical analysis
It is shown that storng blocks, i.e., digraphs that are strongly connected and have no cutnodes have an ear‐decomposition. This result is used to prove that the number q of arcs of minimal strong blocks is bounded by p ≤ q ≤ 2p – 3 and that minimal strong blocks contain at least two nodes with indegree and outdegree equal to one.