Edge‐colored saturated graphs

Abstract

Abstract A graph G is ( k 1 , k 2 , …, k t )‐saturated if there exists a coloring C of the edges of G in t colors 1, 2, …, t in such a way that there is no monochromatic complete k i ‐subgraph K of color i , 1 ⩽ i ⩽ t , but the addition of any new edge of color i , joining two nonadjacent vertices in G , with C , creates a monochromatic K of color i , 1 ⩽ i ⩽ t . We determine the maximum and minimum number of edges in such graphs and characterize the unique extremal graphs.