---
tag: XFWW0NYR6B
kind: concept
name: Paving matroid
sources:
  - wikipedia: en:37729421@r1256718365
    locator: Paving matroid
    note: adopted
    mention: wikipedia://en/37729421
    sections: [Summary]
same_as:
  wikidata: Q7155894
  wikipedia: Paving matroid
inventory: [876E3142F0]
---

## Summary

In the mathematical theory of matroids, a **paving matroid** is a matroid in which every circuit has size at least as large as the matroid's rank. In a matroid of rank $r$ every circuit has size at most $r+1$, so it is equivalent to define paving matroids as the matroids in which the size of every circuit belongs to the set $\{r,r+1\}$. It has been conjectured that [[almost all|N1XSAXCQY3]] matroids are paving matroids.