Recursive local amoeba construction.

Abstract: Amoeba graphs were born as examples of balanceable graphs, which are graphs that appear in any 2-edge coloring of the edges of a large enough $K_n$ with a sufficient amount of red and blue edges. As they were studied further, interesting aspects were found.

An edge replacement $e\to e$ in a labeled graph G means to take an edge e in E(G) and replace it with e’ \in E(\overline{G})\cup \{e\}$. If $G-e+e’$ is isomorphic to $G$ then we say $e\to e’$ is a \emph{feasible edge replacement}. Every edge replacement yields a set of permutations of the labels in $G$. The set of all permutations associated with all feasible edge replacements in $G$ generates the group $\Gamma_G$. A labeled graph $G$ of order $n$ is a \emph{local amoeba} if $\Gamma_G \cong S_n$. One might think local amoebas are hard to find. However, in this talk we will go over a recursive construction of infinite families of local amoebas.

Es trabajo conjunto con Ludmila Matyskova.