Seymour's Second Neighborhood Conjecture (SSNC) asserts that every oriented finite
simple graph (without digons) has a vertex whose second out-neighborhood is at least as …

Abstract k≥ 2 be an integer. A digraph D=(V, E) is k-anti-transitive if for every pair of vertices
u, v∈ V, the existence of a directed path of length k from u to v implies that (u, v)∉ E. Under …

Abstract Seymour's Second Neighborhood Conjecture (SNC) asserts that every oriented
graph has a vertex whose second out-neighborhood is at least as large as its first out …

Abstract Seymour's Second Neighborhood Conjecture (SSNC) asserts that there always
exists a vertex v such that the cardinality of its second out-neighborhood is at least as large …

Abstract Seymour's Second Neighborhood Conjecture states that every simple oriented
graph has a vertex such that the cardinality of its second neighborhood is greater than or …

A digraph $ D=(V, E) $ is $ k $-transitive if for any directed $ uv $-path of length $ k $, we
have $(u, v)\in E $. In this paper, we study the structure of strong $ k $-transitive oriented …

A kernel in a digraph is an independent and absorbent subset of its vertex set. A digraph is
critical kernel imperfect if it does not have a kernel, but every proper induced subdigraph …

Seymour Second Neighborhood Conjecture (SSNC) asserts that every finite oriented graph
has a vertex whose second out-neighborhood is at least as large as its first out …

Let (D=(V, E)) be an oriented graph with minimum out‐degree δ+. For x∈ V (D), let d D+ x
and d D++ x be the out‐degree and second out‐degree of x in D, respectively. For a directed …

Seymour's Second Neighborhood Conjecture asserts that every digraph has a vertex $ v $
whose second out-neighborhood $ N^{++}(v) $ is at least as large as its out-neighborhood …