Abstract
Publisher Summary A well-known result of Gallai and Milgram asserts that the least number of paths that partition the vertex-set X is at most the stability number α(G) (maximum number of independent vertices). For instance, if G is a tournament, that is, α( G ) = 1, then one path suffices to cover the vertex-set, and get the Redei's result. The Gallai-Milgram theorem has been extended independently. Another extension is also presented, which contains both the result of Las Vergnas and those of Linial, and shows some new applications. The problems about the covering of strongly connected graphs with paths or circuits are surveyed. The Las Vergnas conjecture is true for symmetric graphs; the same argument shows also that the Bermond's conjecture is true for symmetric graphs.
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