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Reconnaissance des graphes de cordes. (French) Zbl 0567.05033
A simple graph $$G=(V,E)$$ is a circle graph if one can associate to G a diagram C(V), consisting of a circle C together with a set V of chords of C, in such a way that adjacency of vertices corresponds to crossing of corresponding chords. An orientation of a chord x of C(V) allows us to define the left side and the right side of x. The relation: ”The initial end of the chord x is on the left side of the chord y” associated to an arbitrary orientation of the chords of C(V) gives an orientation of the edges of G and a double labelling of the edges of the complementary graph $$\bar G.$$ The author studies the combinatorial relationships between such an orientation and such a double labelling. A characterization of circle graphs which yields a polynomial time recognition algorithm is also obtained.
Reviewer: Ph.Vincke

MSC:
 05C38 Paths and cycles 05C20 Directed graphs (digraphs), tournaments
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References:
 [1] Bondy, J.A; Murty, U.S.R, Graph theory with applications, (1976), MacMillan London · Zbl 1134.05001 [2] Fournier, J.C, Une caractérisation des graphes de cordes, C.R. acad. sci. Paris, 811-813, (1978) · Zbl 0378.05045 [3] H. De Fraysseix, A characterization of circle-graphs, a paraître. · Zbl 0551.05056 [4] Golumbic, M.C, Algorithmic graph theory and perfect graphs, (1980), Academic Press New York, Ch. 11 · Zbl 0541.05054
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