The class of $(P_7,C_4,C_5)$-free graphs: decomposition, algorithms, and $\chi$-boundedness

Kathie Cameron, Shenwei Huang, Irena Penev +1

As usual, $P_n$ ($n\ge 1$) denotes the path on $n$ vertices, and $C_n$ ($n\ge 3$) denotes the cycle on $n$ vertices. For a family $\mathcal{H}$ of graphs, we say that a graph $…