Edge-colored saturated graphs
暂无分享，去创建一个
A graph G is (k1, k2, …, kt)-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 ki-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.
[1] Paul Erdös,et al. On a Problem in Graph Theory , 1963, The Mathematical Gazette.
[2] Paul Erdös,et al. On a theorem of Rademacher-Turán , 1962 .
[3] J. A. Bondy,et al. Graph Theory with Applications , 1978 .
[4] P. Turán. On the theory of graphs , 1954 .
[5] D. Hanson,et al. Minimal k-saturated and color critical graphs of prescribed minimum degree , 1986, J. Graph Theory.
[6] B. Bollobás. On generalized graphs , 1965 .