Abstract

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 {P2∪P3,house}-free graphs.

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