Post #56

Ringel’s conjecture is proved. Ringel's conjecture states that every complete graph with 2n+1 nodes can be decomposed into a set of any identical non-overlapping trees of order n. In other words, take any tree with n nodes, place it on the complete graph with 2n+1 nodes, remove the edges your tree covers, and continue with the remaining graph. No matter which tree you have started with, there is a procedure to remove all the edges in a complete graph by placing your tree step by step. This conjecture was known for 60 years and finally has been proved last month. At last this article makes a good job explaining how it was done.