The Search for the Smallest 3-E.C. Graphs

Abstract

A graph $G$ is $3$-existentially closed ($3$-e.c.) if each $3$-set of vertices can be extended in all of the possible eight ways. Results which improve the lower bound of the minimum order of a $3$-e.c. graph are reported. It has been shown that $m_{ec}(3)\ge 24$, where $m_{ec}(3)$ is defined to be the minimum order of a $3$-e.c. graph.