Characterization of Circular-arc Graphs: II. McConnell Flipping
Combinatorics
2025-04-30 v3 Data Structures and Algorithms
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 -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.
Cite
@article{arxiv.2408.10892,
title = {Characterization of Circular-arc Graphs: II. McConnell Flipping},
author = {Yixin Cao and Tomasz Krawczyk},
journal= {arXiv preprint arXiv:2408.10892},
year = {2025}
}