This is my favourite paper to come out of my research with Jing Huang at the University of Victoria, and the last one to be published. The main result shows that everything you need to know about monopolar partitions in claw-free graphs can be uncovered by listing some rules for pairs of vertices in the graph and following the direct implications.
We later generalized the proof to a technique we called "colour-bipartitions", but I look back on the original moment of inspiration most fondly.
On the polarity and monopolarity of graphs. Journal of Graph Theory 76(2). Ross Churchley and Jing Huang (2014). ↩︎