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perfect graph

graph whose maximum clique’s size equals the chromatic number
Thing bounded_graph_class Q1187620
perfect graph
David Eppstein at English Wikipedia · Public Domain · Wikimedia
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perfect graph

Summary

perfect graph is a χ-bounded graph class[1]. It draws 139 Wikipedia views per month (bounded_graph_class category, ranking #1 of 1).[2]

Key Facts

  • perfect graph's instance of is recorded as χ-bounded graph class[3].
  • perfect graph's instance of is recorded as intersection class of graphs[4].
  • perfect graph's instance of is recorded as self-complementary graph class[5].
  • perfect graph is a type of odd-anti-hole-free graph[6].
  • perfect graph is a type of odd-hole-free graph[7].
  • perfect graph's topic's main category is recorded as Category:Perfect graphs[8].
  • perfect graph's studied by is recorded as graph theory[9].
  • perfect graph's maintained by WikiProject is recorded as WikiProject Mathematics[10].

Body

Definition and Type

Recorded instance of include χ-bounded graph class[3], intersection class of graphs[4], and self-complementary graph class[5]. Recorded subclass of include odd-anti-hole-free graph[6] and odd-hole-free graph[7].

Why It Matters

perfect graph draws 139 Wikipedia views per month (bounded_graph_class category, ranking #1 of 1).[2] It has Wikipedia articles in 15 language editions, a strong signal of global cultural recognition.[11] It is known by 6 alternative names across languages and contexts.[12]

Related Entities

graph theory

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . Characterizing intersection classes of graphs. wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [11] ↑ . Wikidata sitelinks. wikidata.org.
  3. [12] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). perfect graph. Retrieved May 3, 2026, from https://4ort.xyz/entity/perfect-graph
MLA “perfect graph.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/perfect-graph.
BibTeX @misc{4ortxyz_perfect-graph_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{perfect graph}}, year = {2026}, url = {https://4ort.xyz/entity/perfect-graph}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): perfect graph — https://4ort.xyz/entity/perfect-graph (retrieved 2026-05-03)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 5w ago · Twofivesixbot bot · 2026-05-27 view diff on Wikidata ↗
    Instance of → χ-bounded graph class, intersection class of graphs, self-complementary graph class
    Subclass of → —
    Maintained by wikiproject → WikiProject Mathematics
    Aliases → —
    + 4 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|3 */ [[Property:P8189]]: 987007536193405171, mv to monolingual text names on J9U statements"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.