On Infinite-finite Duality Pairs of Directed Graphs

Péter L. Erdos, Claude Tardif, G. Tardos

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The (A,D) duality pairs play a crucial role in the theory of general relational structures and in Constraint Satisfaction Problems. The case where both sides are finite is fully characterized. The case where both sides are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction that both classes are antichains. In this paper (which is the first one of a series) we start the detailed study of the infinite-finite case. Here we concentrate on directed graphs. We prove some elementary properties of the infinite-finite duality pairs, including lower and upper bounds on the size of D, and show that the elements of A must be equivalent to forests if A is an antichain. Then we construct instructive examples, where the elements of A are paths or trees. Note that the existence of infinite-finite antichain dualities was not previously known.

Original languageEnglish
Pages (from-to)807-819
Number of pages13
JournalOrder
Volume30
Issue number3
DOIs
Publication statusPublished - Nov 2013

Fingerprint

Constraint satisfaction problems
Directed graphs
Directed Graph
Duality
Antichain
Constraint Satisfaction Problem
Upper and Lower Bounds
Restriction
Path
Series

Keywords

  • Constraint satisfaction problem
  • Duality pairs
  • General relational structures
  • Graph homomorphism
  • Nondeterministic finite automaton
  • Regular languages

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

On Infinite-finite Duality Pairs of Directed Graphs. / Erdos, Péter L.; Tardif, Claude; Tardos, G.

In: Order, Vol. 30, No. 3, 11.2013, p. 807-819.

Research output: Contribution to journalArticle

Erdos, Péter L. ; Tardif, Claude ; Tardos, G. / On Infinite-finite Duality Pairs of Directed Graphs. In: Order. 2013 ; Vol. 30, No. 3. pp. 807-819.
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