Characterization of Chordal Circular-arc Graphs: I. Split Graphs
Abstract
The most elusive problem around the class of circular-arc graphs is identifying all minimal graphs that are not in this class. The main obstacle is the lack of a systematic way of enumerating these minimal graphs. McConnell [FOCS 2001] presented a transformation from circular-arc graphs to interval graphs with certain patterns of representations. We fully characterize these interval patterns for circular-arc graphs that are split graphs, thereby building a connection between minimal split graphs that are not circular-arc graphs and minimal non-interval graphs. This connection enables us to identify all minimal split graphs that are not circular-arc graphs. As a byproduct, we develop a linear-time certifying recognition algorithm for circular-arc graphs when the input is a split graph.
Keywords
Cite
@article{arxiv.2403.01947,
title = {Characterization of Chordal Circular-arc Graphs: I. Split Graphs},
author = {Yixin Cao and Jan Derbisz and Tomasz Krawczyk},
journal= {arXiv preprint arXiv:2403.01947},
year = {2025}
}