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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.

Date: Sep 28, 2022 at 15:00:00 h
Venue: Sala de Seminario John Von Neuman, CMM, Beauchef 851, Torre Norte, Piso 7.
Speaker: Denae Ventura
Affiliation: UNAM, México
Coordinator: José Verschae