A patient's skin will most likely become cyanotic due to:

Cyanosis is a bluish discoloration of the skin and mucous membranes that typically occurs when there is a decrease in the amount of oxygen in the blood. This condition arises when the arterial blood oxygen levels drop significantly, leading to inadequate oxygen delivery to the body's tissues. When oxygen saturation falls, the hemoglobin in the blood contains less oxygen, resulting in a darker hue that manifests as cyanosis, particularly visible in areas such as the lips, fingers, and toes.

In contrast, an increase in arterial oxygen would generally result in well-oxygenated blood, leading to a healthy pink coloration of the skin. A rapid heart rate may indicate various physiological responses but does not directly cause cyanosis. Similarly, a lack of blood circulation can lead to other symptoms, but it is the specific decrease in arterial oxygen that is most directly linked to the appearance of cyanosis. Thus, inadequate arterial oxygen levels are the primary cause for this condition.