Involve: A Journal of Mathematics
- Volume 5, Number 1 (2012), 67-80.
Betti numbers of order-preserving graph homomorphisms
For graphs and with totally ordered vertex sets, a function mapping the vertex set of to the vertex set of is an order-preserving homomorphism from to if it is nondecreasing on the vertex set of and maps edges of to edges of . In this paper, we study order-preserving homomorphisms whose target graph is the complete graph on 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 to the complete graph .
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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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