## Hadwiger conjecture (graph theory) |

Unsolved problem in mathematics: |

In **Hadwiger conjecture** (or **Hadwiger's conjecture**) states that, if all *G* use *k* or more colors, then one can find *k* *G* such that each subgraph is connected by an *K _{k}* on

This conjecture, a far-reaching generalization of the ^{[1]}

- equivalent forms
- special cases and partial results
- generalizations
- notes
- references

An equivalent form of the Hadwiger conjecture (the *G* to the complete graph *K _{k}*, then

Note that, in a *k*-coloring of any graph *G*, contracting each color class of the coloring to a single vertex will produce a complete graph *K _{k}*. However, this contraction process does not produce a minor of

If *F _{k}* denotes the family of graphs having the property that all minors of graphs in

The *h*(*G*) of a graph *G* is the size *k* of the largest complete graph *K _{k}* that is a minor of

Other Languages

Deutsch: Hadwigers Vermutung

français: Conjecture de Hadwiger

magyar: Hadwiger-sejtés (gráfelmélet)

русский: Гипотеза Хадвигера (теория графов)

українська: Гіпотеза Хадвігера