English

An inequality on global alliances for trees

Combinatorics 2013-07-23 v1

Abstract

In this paper, we prove an inequality on the cardinalities of the minimum size global defensive alliance and the minimum size global offensive alliance. A global defensive alliance is a dominating set such that when any point inside a selected group SS is chosen, at least half of the points in its neighborhood are also in the set SS, including the selected point. A global offensive alliance is a dominating set such that if any point outside SS is selected, at least half of the points in its neighborhood, including the selected point, are in set SS. Our result answers an open question in [HA].

Cite

@article{arxiv.1307.5808,
  title  = {An inequality on global alliances for trees},
  author = {Alexandria Yu},
  journal= {arXiv preprint arXiv:1307.5808},
  year   = {2013}
}
R2 v1 2026-06-22T00:55:40.285Z