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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

MSC:
05C75 Structural characterization of families of graphs
05A05 Permutations, words, matrices
05B35 Combinatorial aspects of matroids and geometric lattices
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