%0 Journal Article %T 3-Anti-Circulant Digraphs Are <i>¦Á</i>-Diperfect and BE-Diperfect %A Lucas I. B. Freitas %A Orlando Lee %J Open Journal of Discrete Mathematics %P 29-46 %@ 2161-7643 %D 2022 %I Scientific Research Publishing %R 10.4236/ojdm.2022.123003 %X Let D be a digraph. A subset S of V (D) is a stable set if every pair of vertices in S is non-adjacent in D. A collection of disjoint paths \"\" is a path partition of D, if every vertex in V (D) is in exactly one path of \"\". We say that a stable set S and a path partition \"\" are orthogonal if each path of \"\" contains exactly one vertex of S. A digraph D satisfies the ¦Á-property if for every maximum stable set S of D, there exists a path partition \"\" such that S and \"\" are orthogonal. A digraph D is ¦Á-diperfect if every induced subdigraph of D satisfies the ¦Á-property. In 1982, Berge proposed a characterization for ¦Á-diperfect digraphs in terms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee proposed a similar conjecture. A digraph D satisfies the Begin-End-property or BE-property if for every maximum stable set S of D, there exists a path partition \"\" such that 1) S and \"\" are orthogonal and 2) for each path P ¡Ê \"\", either the start or the end of P belongs to S. A digraph D is BE-diperfect if every induced subdigraph of D satisfies the BE-property. Sambinelli, Silva and Lee proposed a characterization for BE-diperfect digraphs in terms of forbidden %K 3-Anti-Circulant Digraph %K Diperfect Digraph %K Berge¡¯s Conjecture %K Begin-End Conjecture %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=117758