Complex sentence: This research on the claw-free graph has proven that there is a complete structure of the claw-free graph and it is proven in the paper titled "The Structure of claw-free Graphs" by Paul Seymour and Maria Chudnovsky.
Split into simpler sentences: This research on the claw-free graph has proven that there is a complete structure of the graph. This has been proven in the paper titled "The Structure of claw-free Graphs" by Paul Seymour and Maria Chudnovsky.