Coloring a graph with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" display="inline" overflow="scroll"><mml:mi>Δ</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:math> colors: Conjectures equivalent to the Borodin–Kostochka conjecture that appear weaker