Remarks on diagonalizable embeddings of graphs

The following result is proved: if a bipartite graph is not a circle graph, then its complement is not a circle graph. The proof uses Naji’s characterization of circle graphs by means of a linear system of equations with unknowns in $GF (2)$ . At the end of this short note I briefly recall the work of François Jaeger on circle graphs.

Existence and nonexistence of universal graphs

Lawrence Moss (1989)

Fundamenta Mathematicae

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Pavol Híc (1992)

Mathematica Slovaca

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