The complete bipartite graph $K_{1,3}$ is known as a claw-graph. A graph $G$ is said to be claw-free it doesn't have an induced subgraph isomorphic to the claw-graph.
We define a graph to be weak claw-free if it doesn't have a subgraph isomorphic to the claw graph. It is immediate that the maximum degree of any vertex in this graph will be equal to two.
I am interested in the question, what more can be said about the structure of such simple graphs and any references regarding this notion will also very helpful.
Kindly share your thoughts.
Thank you.