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H-kernels in H-colored digraphs without (ξ1,ξ,ξ2)-H-subdivisions of C3→

Author

Listed:
  • Hernández-Lorenzana, Felipe
  • Sánchez-López, Rocío

Abstract

Let H be a digraph possibly with loops and D a digraph without loops with a coloring of its arcs c:A(D)→V(H) (D is said to be an H-colored digraph). A directed path W in D is said to be an H-path if and only if the consecutive colors encountered on W form a directed walk in H. A subset N of vertices of D is said to be an H-kernel if (1) for every pair of different vertices in N there is no H-path between them and (2) for every vertex u in V(D)∖N there exists an H-path in D from u to N. Under this definition an H-kernel is a kernel whenever A(H)=∅. The color-class digraph CC(D) of D is the digraph whose vertices are the colors represented in the arcs of D and (i,j)∈A(CC(D)) if and only if there exist two arcs, namely (u,v) and (v,w) in D, such that (u,v) has color i and (v,w) has color j. Since not every H-colored digraph has an H-kernel and V(CC(D))=V(H), the natural question is: what structural properties of CC(D), with respect to the H-coloring, imply that D has an H-kernel?

Suggested Citation

  • Hernández-Lorenzana, Felipe & Sánchez-López, Rocío, 2022. "H-kernels in H-colored digraphs without (ξ1,ξ,ξ2)-H-subdivisions of C3→," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001734
    DOI: 10.1016/j.amc.2022.127089
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