Central facial erythema with overlying greasy, yellowish scale as seen in this patient is feature of:

Greasy, yellowish scale s/o Seborrheic dermatitis Seborrheic dermatitis: greasy scales overlying erythematous patches or plaques. Induration and scale are generally less prominent than in psoriasis, so a clinical overlap between these diseases ("sebopsoriasis"). Site- scalp, face, eyebrows, eye- lids, glabella, and nasolabial folds. Scaling of the external auditory canal is common in seborrheic dermatitis. Seborrheic dermatitis may also develop in the central chest, axilla, groin, submammary folds, and gluteal cleft. Seborrheic dermatitis in infants occurs in the scalp ("cradle cap"), face, or groin. Cradle cap is frequently seen in patients with Parkinson's disease, cerebrovascular accidents, HIV infection.