If the cardiac supply of the vagus nerve is cut, then heart rate increases. 

The vagus nerve, specifically its parasympathetic fibers, plays a crucial role in regulating heart rate. These fibers release acetylcholine, which acts on the heart's sinoatrial (SA) node to slow down the heart rate.

When the cardiac branches of the vagus nerve are cut or impaired, the parasympathetic influence on the heart diminishes. As a result, the heart rate tends to increase because there is less inhibition on the SA node, which normally slows down the heart rate. This can lead to a condition known as tachycardia, where the heart beats at a faster rate than normal.