# $$\varPi $$ -Kernels in Digraphs

## Related Articles

- 4-TRANSITIVE DIGRAPHS I: THE STRUCTURE OF STRONG 4-TRANSITIVE DIGRAPHS. HERNÁNDEZ-CRUZ, CÉSAR // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 2, p247
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v, w âˆˆ V (D), (u, v), (v, w) âˆˆ A(D) implies that (u, w) âˆˆ A(D). This concept can be generalized as follows: A digraph...

- 3-TRANSITIVE DIGRAPHS. Hernández-Cruz, César // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p205
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u; v;w; x) of length 3 in D implies the existence of the arc (u, x) âˆˆ A(D). In this article strong 3-transitive digraphs are...

- On Sullivan's conjecture on cycles in 4-free and 5-free digraphs. Liang, Hao; Xu, Jun // Acta Mathematica Sinica;Jan2013, Vol. 29 Issue 1, p53
For a simple digraph G, let Î²( G) be the size of the smallest subset X âŠ† E( G) such that Gâˆ’X has no directed cycles, and let Î³( G) be the number of unordered pairs of nonadjacent vertices in G. A digraph G is called k-free if G has no directed cycles of length at most k. This...

- A Characterization of Directed Paths. S., Ramya.; M., Nagesh. H. // International Journal of Mathematical Combinatorics;Jun2015, Vol. 2, p144
In this note, the non-trivial connected digraphs D with vertex set V (D) = {v1, v2, ..., vn} satisfying ... are characterized, where d- (vi) and d+ (vi) be the in-degree and out-degree of vertices of D, respectively.

- KERNELS BY MONOCHROMATIC PATHS AND THE COLOR-CLASS DIGRAPH. GALEANA-SÁNCHEZ, HORTENSIA // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 2, p273
No abstract available.

- k-KERNELS IN GENERALIZATIONS OF TRANSITIVE DIGRAPHS. GALEANA-SÁNCHEZ, HORTENSIA; HERNÁNDEZ-CRUZ, CÉSAR // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 2, p293
No abstract available.

- Î³-CYCLES AND TRANSITIVITY BY MONOCHROMATIC PATHS IN ARC-COLOURED DIGRAPHS. CASAS-BAUTISTA, ENRIQUE; GALEANA-SÁNCHEZ, HORTENSIA; ROJAS-MONROY, ROCÍO // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 3, p493
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a âˆˆ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A Î³-cycle in D is a...

- A Contribution to the Second Neighborhood Problem. Ghazal, Salman // Graphs & Combinatorics;Sep2013, Vol. 29 Issue 5, p1365
Seymour's Second Neighborhood Conjecture asserts that every oriented graph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We...

- SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS. SINHA, DEEPA; GARG, PRAVIN // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p625
A signed graph (or sigraph in short) is an ordered pair S = (SuÎ´), where Su is a graph G = (V,E), called the underlying graph of S and Î´ : E â†’ {+,-} is a function from the edge set E of Suinto the set {+,-}, called the signature of S. The x-line sigraph of S denoted by L x (S) is a...