Title: Coloring (P5, gem)-free graphs with ∆ − 1 colors.

Abstract:   The Borodin–Kostochka Conjecture states that for a graph G, if ∆(G) ≥ 9 and ω(G) ≤ ∆(G)−1, then χ(G) ≤ ∆(G)−1. This conjecture is a strengthening of Brooks' Theorem and while known for certain graph classes it remains open for general graphs. In this talk we prove the Borodin– Kostochka Conjecture for (P5,gem)-free graphs, i.e. graphs with no induced P5 and no induced K1 ∨ P4.