KnowraOdd cycleLinked fromLinked fromThe 8 pages that link to Odd cycle, each with the reason it gives.All 8Broader topic 4Related 3Compared with 1Bipartite graphBroader topic: Any odd cycle proves that a graph cannot be divided into two independent vertex sets.Brooks' theoremRelated: Odd cycles are the other exception, though their chromatic number is three.Vizing's theoremBroader topic: Its maximum degree is two, but its edges require three colors, attaining the upper bound.Kőnig's theoremRelated: Odd cycles obstruct bipartiteness and illustrate why the matching-cover equality cannot extend to all graphs.Blossom algorithmBroader topic: An odd alternating cycle can obstruct the search until contracted into a blossom.Conway's thrackle conjectureRelated: Odd cycles are a central structure in known thrackle arguments.De Bruijn–Erdős theorem (graph theory)Broader topic: An odd cycle is a finite obstruction to two-colorability, so it also obstructs two-colorability in any graph containing it.Erdős–Gyárfás conjectureCompared with: Odd cycles alone cannot meet the conjecture's required length condition.