---
tag: QMKYNQM68Q
kind: concept
name: Helly family
aliases: [helly-property]
sources:
  - wikipedia: en:670453@r1351706773
    locator: Helly family
    note: adopted
    mention: wikipedia://en/670453
    sections: [Summary]
same_as:
  wikidata: Q1603101
  wikipedia: Helly family
inventory: [4YRZ0VDEJ2]
---

## Summary

In [[combinatorics|0JKW7W7XFR]], a **Helly family** of order $k$ is a family of [[sets|0BSJ7RQ9BW]] in which every minimal *subfamily with an empty [[intersection|0ZNMMA9TF5]]* has $k$ or fewer sets in it. Equivalently, every finite subfamily such that every $k$-fold intersection is non-empty has non-empty total intersection. The **$k$-Helly property** is the property of being a Helly family of order $k$.