Square-free graphs with no six-vertex induced path
SIAM Journal on Discrete Mathematics
We elucidate the structure of (P6, C4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes of graphs. Using this result, we show that for any (P6, C4)-free graph G, [Formula presented]\ are tight upper bounds for the chromatic number of G. Moreover, our structural results imply that every (P6,C4)-free 2 graph with no clique cutset has bounded clique-width, and thus the existence of a polynomial-time algorithm that computes the chromatic number (or stability number) of any (P6, C4)-free graph.
Karthick, T. and Maffray, Frédéric, "Square-free graphs with no six-vertex induced path" (2019). Journal Articles. 1038.