Involve: A Journal of Mathematics

  • Involve
  • Volume 5, Number 1 (2012), 67-80.

Betti numbers of order-preserving graph homomorphisms

Lauren Guerra and Steven Klee

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For graphs G and H with totally ordered vertex sets, a function mapping the vertex set of G to the vertex set of H is an order-preserving homomorphism from G to H if it is nondecreasing on the vertex set of G and maps edges of G to edges of H. In this paper, we study order-preserving homomorphisms whose target graph H is the complete graph on n vertices. By studying a family of graphs called nonnesting arc diagrams, we are able to count the number of order-preserving homomorphisms (and more generally the number of order-preserving multihomomorphisms) mapping any fixed graph G to the complete graph Kn.

Article information

Involve, Volume 5, Number 1 (2012), 67-80.

Received: 27 May 2011
Accepted: 11 July 2011
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 05A18: Partitions of sets 06A06: Partial order, general 05C30: Enumeration in graph theory

graph homomorphisms Betti numbers nonnesting partitions


Guerra, Lauren; Klee, Steven. Betti numbers of order-preserving graph homomorphisms. Involve 5 (2012), no. 1, 67--80. doi:10.2140/involve.2012.5.67.

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