1 research outputs found
-anti-circulant digraphs are -diperfect and BE-diperfect
Let be a digraph. A subset of is a stable set if every pair of
vertices in is non-adjacent in . A collection of disjoint paths
of is a path partition of , if every vertex in
is exactly on a path of . We say that a stable set and a path
partition are orthogonal if each path of contains exactly one
vertex of . A digraph satisfies the -property if for every
maximum stable set of , there exists a path partition such
that and are orthogonal. A digraph is -diperfect
if every induced subdigraph of satisfies the -property. In 1982,
Claude Berge proposed a characterization for -diperfect digraphs in
terms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee
proposed a similar conjecture. A digraph satisfies the Begin-End-property
or BE-property if for every maximum stable set of , there exists a path
partition such that (i) and are orthogonal and
(ii) for each path , either the start or the end of
belongs to . A digraph is BE-diperfect if every induced subdigraph of
satisfies the BE-property. Sambinelli, Silva and Lee proposed a
characterization for BE-diperfect digraphs in terms of forbidden blocking odd
cycles. In this paper, we verified both conjectures for -anti-circulant
digraphs. We also present some structural results for -diperfect and
BE-diperfect digraphs.Comment: arXiv admin note: substantial text overlap with arXiv:2111.1216