On kernels by rainbow paths in arc-coloured digraphs

Γ-cycles and Transivity by Monochromatic Paths in Arc-coloured Digraphs

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 ∈ 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 γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . . , un), such that ui 6= uj if i 6= j and for every i ∈ {0, 1, . . . ...

Kernels in the closure of coloured digraphs

Let D be a digraph with V (D) and A(D) the sets of vertices and arcs of D, respectively. A kernel of D is a set I ⊂ V (D) such that no arc of D joins two vertices of I and for each x ∈ V (D) \ I there is a vertex y ∈ I such that (x, y) ∈ A(D). A digraph is kernel-perfect if every non-empty induced subdigraph of D has a kernel. If D is edge coloured, we define the closure ξ(D) of D the multidigr...

Arc-Disjoint Paths in Expander Digraphs

Arc-Disjoint Paths in Decomposable Digraphs

4 We prove that the weak k-linkage problem is polynomial for every fixed k for totally Φ5 decomposable digraphs, under appropriate hypothesis on Φ. We then apply this and recent results 6 by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence 7 number or bounded cut-width) to get polynomial algorithms for some class of digraphs like quasi8 transitive digraphs...

Kernels by monochromatic paths in digraphs with covering number 2

We call the digraph D an m-colored digraph if the arcs of D are colored with m colors. A subdigraph H of D is called monochromatic if all of its arcs are colored alike. A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u, v ∈ N there is no monochromatic directed path between them and; (ii) for eve...