Recursive constructions of amoebas

Global amoebas are a wide and rich family of graphs that emerged from the study certain Ramsey-Turán problems in 2-colorings edges complete graph Kn deal with appearance unavoidable patterns once amount each color is guaranteed. Indeed, it turns out that, as soon such coloring constraints satisfied if n sufficiently large, then every global amoeba can be found embedded has half its color. Even more surprising, bipartite G tonal-variation, meaning for any pair integers r, b r + number G, there subgraph isomorphic to first second. The feature makes work one-by-one edge replacements leave structure invariant. By means group theoretical approach, dynamics this modeled. As counterpart “live” inside possibly large Kn, we also consider local which spanning subgraphs same feature. In an effort highlight their richness versatility, present here three different recursive constructions amoebas, two them yielding interesting families per se one offering range possibilities.