2022/06/09 by Dávid Kunszenti-Kovács, László Lovász, Kunszenti-Kovács, Dávid +3 · 2 citations
Computer Science · Mathematics · #05C80 #28A50 #47B15 (Secondary) #60J99 (Primary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Limits and Structures in Graph Theory #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2206.04493
openalex publication_date 2022/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure on maps of a finite graph into a Markov space. The existence of such homomorphism measures is not always guaranteed, but can be established under rather natural smoothness conditions on the Markov space and sparseness conditions on the graph. This continues a direction in graph limit theory in which such measures are viewed as limits of graph sequences.