Bipartite graphs that are not circle graphs
Annales de l'Institut Fourier, Volume 49 (1999) no. 3, p. 809-814

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.

Nous prouvons le résultat suivant : si un graphe biparti n’est pas un graphe de cordes, alors son complément n’est pas un graphe de cordes. La preuve fait appel à une caractérisation des graphes de cordes par Naji, qui utilise un système d’équations linéaires sur le corps à deux éléments.

À la fin de cette note je rappelle brièvement le travail de François Jaeger sur les graphes de cordes.

@article{AIF_1999__49_3_809_0,
     author = {Bouchet, Andr\'e},
     title = {Bipartite graphs that are not circle graphs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {3},
     year = {1999},
     pages = {809-814},
     doi = {10.5802/aif.1693},
     zbl = {0917.05064},
     mrnumber = {2000g:05127},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_3_809_0}
}
Bouchet, André. Bipartite graphs that are not circle graphs. Annales de l'Institut Fourier, Volume 49 (1999) no. 3, pp. 809-814. doi : 10.5802/aif.1693. http://www.numdam.org/item/AIF_1999__49_3_809_0/

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