A graph is called monopolar if its vertices can be partitioned into an independent set and a disjoint union of cliques. My undergraduate research with Jing Huang studied monopolar partitions in line graphs, claw-free graphs, and other graph classes.

I presented our results at various conferences and seminars, and you can find the slides of each below:

Monopolar partitions: easy to learn, NP-hard to master

UVic discrete math seminar (September 27, 2010)

Monopolar claw-free graphs: characterization and recognition

UVic discrete math seminar (October 25, 2010)

Monopolar claw-free graphs

Canadian Mathematics Society Winter Meeting (December 4, 2010)

Partitioning graphs via edge-coloured homomorphisms

Canadian Discrete and Algorithmic Mathematics Conference (June 1, 2011)

A survey on monopolar graphs: algorithms and complexity

SFU computer science seminar (June 13, 2013)