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2012 Betti numbers of order-preserving graph homomorphisms
Lauren Guerra, Steven Klee
Involve 5(1): 67-80 (2012). DOI: 10.2140/involve.2012.5.67

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.

Citation

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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

Information

Received: 27 May 2011; Accepted: 11 July 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1246.13017
MathSciNet: MR2924315
Digital Object Identifier: 10.2140/involve.2012.5.67

Subjects:
Primary: 13D02
Secondary: 05A18, 05C30, 06A06

Rights: Copyright © 2012 Mathematical Sciences Publishers

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