Open Research Index

Graphic sequences: the Erdős–Gallai and Havel–Hakimi theorems

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-16-000017Oct 16, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the two classical characterizations of degree sequences of finite simple graphs: the Erdős–Gallai theorem (a non-increasing sequence is graphic if and only if its sum is even and every initial segment satisfies the Erdős–Gallai inequality) and the Havel–Hakimi theorem (a non-increasing sequence is graphic if and only if its first term is at most the number of remaining terms, the next d₀ terms are positive, and the reduced sequence is graphic).

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-10-16-000017
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-16-000017/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-16-000017/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'