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Triangle-free graph

In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally independent graphs.

Triangle finding problem, Coloring triangle-free graphs & Independence number and Ramsey theory

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Triangle finding problem

Independence number and Ramsey theory

Coloring triangle-free graphs

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Map overview Semantic statistics

Triangle-free graph

Nodes43
Edges42
Triples32
Avg. degree1.95
Density0.046512
Components1

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Triangle-free graph

Top relations

related to Coloring triangle-free graphs · 18
Triangle-free graph → Blanche Descartes, Every, From, Gimbel, Grötzsch, Grötzsch's, However, If, In, Much, Mycielski, Mycielski's, Mycielskian, Nilli, The, This, Thomassen, Tutte
related to Independence number and Ramsey theory · 9
Triangle-free graph → An, It, Omega, One, Ramsey, These, Theta, This, With
see also · 4
Triangle-free graph → Andrásfai, Kneser, Monochromatic, Szemerédi
is a · 1
Triangle-free graph → undirected graph in which no three vertices form a triangle of edges

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Important terminology

triangle-free graph graphs triangle displaystyle number vertices possible edges vertex colors independent n-vertex time omega neighbors must three form may

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Triangle-free graphis aundirected graph in which no three vertices form a triangle of edges0.90text
Triangle-free graphrelated to Coloring triangle-free graphsMuch0.60section
Triangle-free graphrelated to Coloring triangle-free graphsEvery0.60section
Triangle-free graphrelated to Coloring triangle-free graphsGrötzsch's0.60section
Triangle-free graphrelated to Coloring triangle-free graphsHowever0.60section
Triangle-free graphrelated to Coloring triangle-free graphsThe0.60section
Triangle-free graphrelated to Coloring triangle-free graphsTutte0.60section
Triangle-free graphrelated to Coloring triangle-free graphsBlanche Descartes0.60section
Triangle-free graphrelated to Coloring triangle-free graphsThis0.60section
Triangle-free graphrelated to Coloring triangle-free graphsFrom0.60section
Triangle-free graphrelated to Coloring triangle-free graphsMycielski0.60section
Triangle-free graphrelated to Coloring triangle-free graphsMycielskian0.60section

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    Min side: 3
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