00716452

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00716452 Guo, Yubao Volkmann, Lutz On complementary cycles in locally semicomplete digraphs. Discrete Math. 135, No.1-3, 121-127 (1994). 1994 Elsevier Science B.V. (North-Holland), Amsterdam EN complementary cycles dicycle cover locally semicomplete digraphs tournament dicycle

doi:10.1016/0012-365X(93)E0099-P

A digraph $D$ is locally semicomplete if for each vertex $x$ in $D$ the subdigraphs induced by the positive and negative neighbor sets of $x$ are both semicomplete. This paper gives the following result about 2- connected locally semicomplete digraphs: Such digraphs do not have their vertex set partitioned by two complementary dicycles if and only if they are 2-diregular and have odd order. From this theorem follow two conjectures of Bang-Jensen giving conditions for a 2-connected local tournament $D$ to have a dicycle $C$ such that $D- V(C)$ is strong. N.F.Quimpo (Manila)