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Diamond-Free Circle Graphs are Helly Circle

Jean Daligault 1 Daniel Gonçalves 1 Michaël Rao 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The \emph{diamond} is the graph obtained from $K_4$ by deleting an edge. \emph{Circle graphs} are the intersection graphs of chords in a circle. Such a circle model has the \emph{Helly property} if every three pairwise intersecting chords intersect in a single point, and a graph is \emph{Helly circle} if it has a circle model with the Helly property. We show that the Helly circle graphs are the diamond-free circle graphs, as conjectured by Durán. This characterization gives an efficient recognition algorithm for Helly circle graphs.
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Submitted on : Tuesday, November 17, 2009 - 3:44:24 PM
Last modification on : Thursday, February 7, 2019 - 2:51:35 PM
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Jean Daligault, Daniel Gonçalves, Michaël Rao. Diamond-Free Circle Graphs are Helly Circle. Discrete Mathematics, Elsevier, 2010, 310 (4), pp.845-849. ⟨10.1016/j.disc.2009.09.022⟩. ⟨lirmm-00432897⟩



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