Coloring [formula omitted]-free graphs with [formula omitted] colors.

A house is the graph that consists of an induced 4-vertex cycle and a single vertex with precisely two adjacent neighbors on the cycle. The Borodin–Kostochka Conjecture states that for each graph G with Δ (G) ≥ 9 , we have χ (G) ≤ max { Δ (G) − 1 , ω (G) }. We show that this conjecture holds for { P 2 ∪ P 3 , house } -free graphs. [ABSTRACT FROM AUTHOR]