Sperner's problem for G-independent families
Combinatorics
2013-10-08 v2
Abstract
Given a graph G, let Q(G) denote the collection of all independent (edge-free) sets of vertices in G. We consider the problem of determining the size of a largest antichain in Q(G). When G is the edge-less graph, this problem is resolved by Sperner's Theorem. In this paper, we focus on the case where G is the path of length n-1, proving the size of a maximal antichain is of the same order as the size of a largest layer of Q(G).
Cite
@article{arxiv.1302.6039,
title = {Sperner's problem for G-independent families},
author = {Victor Falgas-Ravry},
journal= {arXiv preprint arXiv:1302.6039},
year = {2013}
}
Comments
26 pages