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Sperner's Problem for G-Independent Families

Published online by Cambridge University Press:  15 October 2014

VICTOR FALGAS-RAVRY
VICTOR FALGAS-RAVRY*
Affiliation:
Institutionen för matematik och matematisk statistik, Umeå Universitet, 901 87 Umeå, Sweden (e-mail: [email protected])
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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 edgeless 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 that the size of a maximal antichain is of the same order as the size of a largest layer of Q(G).

Keywords

Primary 05D05
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 3 , May 2015 , pp. 528 - 550
Copyright
Copyright © Cambridge University Press 2014 

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