Erdős–Faber–Lovász conjecture states that if a graph G is a union of the n edge-disjoint copies of complete graph Kn, that is, each pair of complete graphs has at most one shared vertex, then the chromatic number of graph G is n. In fact, we only need to consider the graphs where each pair of complete graphs has exactly one shared vertex. However, each shared vertex may be shared by more than two complete graphs. Therefore, this paper first considers the graphs where each shared vertex happens to be shared by two complete graphs, and then d...
