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arXiv · 2408.10892

Characterization of Circular-arc Graphs: II. McConnell Flipping

Yixin Cao·Tomasz Krawczyk
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Abstract

McConnell [FOCS 2001] presented a flipping transformation from circular-arc graphs to interval graphs with certain patterns of representations. Beyond its algorithmic implications, this transformation is instrumental in identifying all minimal graphs that are not circular-arc graphs. We conduct a structural study of this transformation, and for $C_{4}$-free graphs, we achieve a complete characterization of these patterns. This characterization allows us, among other things, to identify all minimal chordal graphs that are not circular-arc graphs in a companion paper.

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Yixin Cao, Tomasz Krawczyk. 2025-04-29. Characterization of Circular-arc Graphs: II. McConnell Flipping. https://arxiv.org/abs/2408.10892

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