Duffus, D.; Erdős, P. L.; Nešetřil, J.; Soukup, L. Antichains in the homomorphism order of graphs. (English) Zbl 1199.06008 Commentat. Math. Univ. Carol. 48, No. 4, 571-583 (2007). Summary: Let \(\mathbb G\) and \(\mathbb D\), respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order-theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal antichains in \(\mathbb G\) and in \(\mathbb D\). The splitting maximal antichains give infinite versions of dualities for graphs and for directed graphs. Cited in 1 ReviewCited in 4 Documents MSC: 06A07 Combinatorics of partially ordered sets 05C99 Graph theory Keywords:partially ordered set; homomorphism order; duality; antichain; splitting property PDFBibTeX XMLCite \textit{D. Duffus} et al., Commentat. Math. Univ. Carol. 48, No. 4, 571--583 (2007; Zbl 1199.06008) Full Text: EuDML EMIS