?-Kernels in Digraphs
Por:
Galeana-Sánchez H., Montellano-Ballesteros J.J.
Publicada:
1 ene 2014
Resumen:
Let $$D=(V(D), A(D))$$D=(V(D),A(D)) be a digraph, $$DP(D)$$DP(D) be the set of directed paths of $$D$$D and let $$\varPi $$? be a subset of $$DP(D)$$DP(D). A subset $$S\subseteq V(D)$$S?V(D) will be called $$\varPi $$?-independent if for any pair $$\{x, y\} \subseteq S$${x,y}?S, there is no $$xy$$xy-path nor $$yx$$yx-path in $$\varPi $$?; and will be called $$\varPi $$?-absorbing if for every $$x\in V(D)\setminus S$$x?V(D)\S there is $$y\in S$$y?S such that there is an $$xy$$xy-path in $$\varPi $$?. A set $$S\subseteq V(D)$$S?V(D) will be called a $$\varPi $$?-kernel if $$S$$S is $$\varPi $$?-independent and $$\varPi $$?-absorbing. This concept generalize several “kernel notions” like kernel or kernel by monochromatic paths, among others. In this paper we present some sufficient conditions for the existence of $$\varPi $$?-kernels. © 2014, Springer Japan.
Filiaciones:
Galeana-Sánchez H.:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico, D.F. 04510, Mexico
Montellano-Ballesteros J.J.:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico, D.F. 04510, Mexico
|