## Involve: A Journal of Mathematics

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

### Betti numbers of order-preserving graph homomorphisms

#### Abstract

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

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

Dates
Accepted: 11 July 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513733450

Digital Object Identifier
doi:10.2140/involve.2012.5.67

Mathematical Reviews number (MathSciNet)
MR2924315

Zentralblatt MATH identifier
1246.13017

#### Citation

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. https://projecteuclid.org/euclid.involve/1513733450

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