A Glance at Graph Theory—part Ii

This survey emphasises results in graph theory which were fairly difficult to prove. Because it is a personal view of the subject, this section will describe three of my own results which I personally found fairly difficult to prove (whatever their degree of difficulty in an absolute sense may be). A decomposition of a graph G is a set of subgraphs of G such that each edge of G belongs to exactly one of these subgraphs. We say that G is decomposable into circuits if it has a decomposition 3) such that all the subgraphs belonging to 3) are circuits. For example, the graph in Fig. 23 is decomposable into five circuits C1,C2,C3,C4,CS