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A characterization of circle graphs. (English) Zbl 0551.05056
A double occurrence sequence is a finite sequence of letters on an alphabet, defined up to a circular permutation, such that each letter has exactly two occurrences in S. A simple graph is a circle graph if it is the interlacement graph of a double-occurrence sequence. A circle graph can be viewed as a chord intersection graph. The author proves that a connected graph is a circle graph if and only if it is a cocyclic-path intersection graph (simple graph with vertex set being a family of cocyclic paths of a given graph, two vertices being adjacent if and only if the corresponding cocyclic paths have an edge in common). He restates this result in terms of matroid theory.
Reviewer: G.Chaty

05C75 Structural characterization of families of graphs
05A05 Permutations, words, matrices
05B35 Combinatorial aspects of matroids and geometric lattices
Full Text: DOI
[1] Even, S.; Itai, A., Queues, stacks and graphs, (), 71-86
[2] Fournier, J.C., Une caractérisation des graphes de cordes, C.R. acad. sci. Paris, 286A, 811-813, (1978) · Zbl 0378.05045
[3] de Fraysseix, H., Local complementation and interlacement graphs, Discrete math., 33, 1, 29-35, (1981) · Zbl 0448.05024
[4] F. Jaeger, Graphes de cordes et espaces graphiques, (to appear). · Zbl 0542.05055
[5] Rosenstiehl, P., Caractérisation des graphes planaires par une diagonale algèbrique, C. R. acad. sci. Paris, 283A, 417-419, (1976) · Zbl 0355.05019
[6] Rosenstiehl, P., Solution algèbrique du problème de Gauss sur la permutation des points d’intersection d’une ou plusieurs courbes fermées du plan, C.R. acad. sci. Paris, 283A, 551-553, (1976) · Zbl 0345.05130
[7] Rosenstiehl, P.; Read, R.C., On the principal edge tripartition of a graph, Ann. discrete math., 3, 195-226, (1978) · Zbl 0392.05059
[8] Touchard, J., Sur un problème de configuration et sur LES fractions continues, Canad. J. math., 4, 2-25, (1952) · Zbl 0047.01801
[9] Welsh, D.J.A., Matroid theory, (1976), Academic Press London · Zbl 0343.05002
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