Abstract
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 .
Citation
Lauren Guerra. Steven Klee. "Betti numbers of order-preserving graph homomorphisms." Involve 5 (1) 67 - 80, 2012. https://doi.org/10.2140/involve.2012.5.67
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