# The theorems of König and Menger

Chapter

## Abstract

Many of our graphs in the previous chapters had the property that their point set *V(G)* decomposed into two disjoint sets *X* _{1} and *X* _{2} and every edge connected one point of *X* _{1} to one of *X* _{2}. Such graphs are called *bipartite* graphs with *bipartition* *X* _{1}, *X* _{2}. A simple bipartite graph with bipartition *X* _{1}, *X* _{2} where |*X* _{1}| = *k*, |*X* _{2}| = ℓ is called a *complete bipartite graph* and is denoted by *K* _{ k,ℓ } if every point of *X* _{1} is adjacent to every point of *X* _{2}. For example, *K* _{3,3} is the second Kuratowski graph.

### Keywords

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1989