Quasi-kernels and quasi-sinks in infinite graphs
Combinatorics
2007-12-06 v1
Abstract
Given a directed graph G=(V,E) an independent set A of the vertices V is called quasi-kernel (quasi-sink) iff for each point v there is a path of length at most 2 from some point of A to v (from v to some point of A). Every finite directed graph has a quasi-kernel. The plain generalization for infinite graphs fails, even for tournaments. We investigate the following conjecture here: for any digraph G=(V,E) there is a a partition (V_0,V_1) of the vertex set such that the induced subgraph G[V_0] has a quasi-kernel and the induced subgraph G[V_1] has a quasi-sink.
Cite
@article{arxiv.0712.0663,
title = {Quasi-kernels and quasi-sinks in infinite graphs},
author = {Peter L. Erdos and Lajos Soukup},
journal= {arXiv preprint arXiv:0712.0663},
year = {2007}
}