---
tag: 2SG37J430M
kind: statement
role: proposition
name: Rosa's Conjecture
sources:
  - wikipedia: en:9944209@r1374720138
    locator: Cactus graph, section Triangular cactus > Rosa's Conjecture
    note: adopted
    mention: wikipedia://en/9944209#YYLS
    sections: [Statement]
inventory: [7HD976CGJX]
---

## Statement

An important conjecture related to the triangular cactus is the **Rosa's Conjecture**, named after **Alexander Rosa**, which says that all triangular cacti are graceful or nearly-graceful. More precisely

*All triangular cacti with t ≡ 0, 1 mod 4 blocks are graceful, and those with t ≡ 2, 3 mod 4 are near graceful.*