Graphs with (strong) proper connection numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"><mml:mrow><mml:mi>m</mml:mi><mml:mo linebreak="goodbreak">−</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si19.svg"><mml:mrow><mml:mi>m</mml:mi><mml:mo linebreak="goodbreak">−</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>

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