Antichains and duality pairs in the digraph-poset

Let D denote the partially ordered sets of homomorphism classes of finite directed graphs, ordered by the homomorphism relation. Order theoretic properties of this poset have been studied extensively, and have interesting connections to familiar graph properties and parameters. This paper studies the generalized duality pairs in D.

[1]  A. Leaf.  GRAPH THEORY AND PROBABILITY , 1957 .

[2]  P. Erdos,et al.  On chromatic number of graphs and set-systems , 1966 .

[3]  Jaroslav Nesetril,et al.  Duality Theorems for Finite Structures (Characterising Gaps and Good Characterisations) , 2000, J. Comb. Theory, Ser. B.

[4]  Péter L. Erdös,et al.  How To Split Antichains In Infinite Posets* , 2007, Comb..

[5]  Jaroslav Nesetril,et al.  On sparse graphs with given colorings and homomorphisms , 2004, J. Comb. Theory, Ser. B.

[6]  Vojtech Rödl,et al.  Chromatically optimal rigid graphs , 1989, J. Comb. Theory B.

[7]  A. Pultr,et al.  Combinatorial, algebraic, and topological representations of groups, semigroups, and categories , 1980 .

[8]  Rudolf Ahlswede,et al.  A splitting property of maximal antichains , 1995, Comb..

[9]  Claude Tardif,et al.  Generalised Dualities and Finite Maximal Antichains , 2006, WG.

[10]  Jaroslav Nesetril,et al.  On maximal finite antichains in the homomorphism order of directed graphs , 2003, Discuss. Math. Graph Theory.

[11]  Jaroslav Nesetril,et al.  On Finite Maximal Antichains in the Homomorphism Order , 2007, Electron. Notes Discret. Math..

[12]  Jaroslav Nesetril,et al.  Universal partial order represented by means of oriented trees and other simple graphs , 2005, Eur. J. Comb..

[13]  P. Erdos,et al.  On chromatic number of graphs and set-systems , 1966 .

[14]  Dwight Duffus,et al.  Antichains in the homomorphism order of graphs , 2007 .

[15]  Xuding Zhu,et al.  Duality and Polynomial Testing of Tree Homomorphisms , 1996 .

[16]  Jaroslav Nesetril,et al.  On classes of relations and graphs determined by subobjects and factorobjects , 1978, Discret. Math..

[17]  Jaroslav Nesetril,et al.  Generalised dualities and maximal finite antichains in the homomorphism order of relational structures , 2008, Eur. J. Comb..