Abstract
A normal Helly circular-arc graph is the intersection graph of arcs on a circle of which no three or less arcs cover the whole circle. Lin et al. [Discrete Appl. Math. 2013] presented the first recognition algorithm for this graph class by characterizing circular-arc graphs that are not in it. They posed as an open problem to design a direct recognition algorithm, which is resolved by the current paper. When the input is not a normal Helly circular-arc graph, our algorithm finds in linear time a minimal forbidden induced subgraph. Grippo and Safe [arXiv:1402.2641] recently reported the forbidden induced subgraphs characterization of normal Helly circular-arc graphs. The correctness proof of our algorithm provides, as a byproduct, an alternative proof to this characterization.
Supported by ERC under the grant 280152 and OTKA under the grant NK105645.
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Cao, Y. (2014). Direct and Certifying Recognition of Normal Helly Circular-Arc Graphs in Linear Time. In: Chen, J., Hopcroft, J.E., Wang, J. (eds) Frontiers in Algorithmics. FAW 2014. Lecture Notes in Computer Science, vol 8497. Springer, Cham. https://doi.org/10.1007/978-3-319-08016-1_2
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DOI: https://doi.org/10.1007/978-3-319-08016-1_2
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