---
tag: G6VPTH1EFR
kind: concept
name: Critical
sources:
  - wikipedia: en:325802@r1373839425
    locator: Glossary of graph theory, section C
    note: adopted
    mention: wikipedia://en/325802#JDTQ
    sections: [Summary]
inventory: [1KPBEX28SV]
---

## Summary

A critical graph for a given property is a graph that has the property but such that every subgraph formed by deleting a single vertex does not have the property. For instance, a factor-critical graph is one that has a perfect matching (a 1-factor) for every vertex deletion, but (because it has an odd number of vertices) has no perfect matching itself. Compare *hypo-*, used for graphs which do not have a property but for which every one-vertex deletion does.