Work

A Very Short Proof of Sidorenko’s Inequality for Counts of Homomorphisms Between Graphs

Year: 2025

Type: article

Abstract: A fundamental extremality result due to Sidorenko [‘A partially ordered set of functionals corresponding to graphs’, Discrete Math. 131 (1–3) (1994), 263–277] states that among all connected graphs G on k vertices, the k -vertex star maximises the number of graph homomorphisms of G into any graph H . We provide a new short proof of this result using only a simple recursive counting argument for trees and Hölder’s inequality.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s000497272500019x

Authors: LUKAS LÜCHTRATH, CHRISTIAN MÖNCH

Institutions: Weierstrass Institute for Applied Analysis and Stochastics, Johannes Gutenberg University Mainz

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,550

Funders: Deutsche Forschungsgemeinschaft, Leibniz-Gemeinschaft