Following the conjecture of Babai, one could propose a counterconjecture (in which I personally do not believe): Counterconjecture 3: For every positive integer k, there are infinitely many connected ...

be connected to each other by an edge — equivalent to people at a party who may (or may not) have met before. The size of a graph is set by n, the number of vertices it has. A portion of a graph in ...

Draw edges between them so that every vertex is connected to every other vertex ... the central vertex aligns with one of the vertices in the complete graph. You’ll cover some but not all of the edges ...

For the Königsberg Bridge graph (Fig. 1b), this is not the ... touching the vertex lead into it and half lead out from it. It is a bit harder to see the converse—that every connected balanced ...