Ringel’s question was about the relationship between complete graphs and trees. He said: First imagine a complete graph containing 2n + 1 vertices (that is, an odd number). Then think about every ...

TREE(3) is one of those examples. ... What exactly does this mean? To put it another way: If you make a tree graph that contains a previous smaller tree graph, the game ends.

A shorter direct proof of that result was obtained by Geelen, Gerards, and Whittle [GGW00p]. However, to prove Theorem 7.0.1, the well-quasi-ordering for graphs of bounded tree-width is needed only ...

Circles are an effective way to show distances from a point making this application an exception to my usual criticism of circles and bubbles in graphs.