Delta-conjecture (1978)

Source placement record

Delta-conjecture (1978): consider a complete graph ( V ; E 1 , … , E d ) {\displaystyle (V;E_{1},\dots ,E_{d})} {\displaystyle (V;E_{1},\dots ,E_{d})} each edge of which is colored by one of d {\displaystyle d} {\displaystyle d} colors such that there exists a triangle Δ {\displaystyle \Delta } {\displaystyle \Delta } colored in three pairwise distinct colors. Then, in each chromatic component ( V , E i ) , i = 1 , … , d {\displaystyle (V,E_{i}),i=1,\dots ,d} {\displaystyle (V,E_{i}),i=1,\dots ,d}, one can choose a maximal independent vertex-set such that the intersection of the obtained d {\displaystyle d} {\displaystyle d} sets is empty.

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Source status: Open
Field: Graph theory · Miscellaneous graph theory
Record type: Revision-pinned source placement
Verification: Source-index reviewed
Source grade: secondary
Reviewed: 2026-07-27T18:04:33.834Z

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Wikipedia list subsection — Exact Graph theory › Miscellaneous graph theory subsection in the revision-pinned source.
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Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.