Reducing prime graphs and recognizing circle graphs
A reduction theorem for prime (simple) graphs in \textit{W. H. Cunningham}'s sense [SIAM J. Algebraic Discrete Methods 3, 214-228 (1982; Zbl 0497.05031)] is presented. It says that every prime graph of order \(n>5\) contains a smaller prime graph of order n-1. As an application a polynomial algorithm for recognizing circle graphs in \((n^ 5)\) time is presented.
scientific article; zbMATH DE number 4089581
scientific article