Sales and earnings at three major retailing chains increased during the third quarter over the figures for 1978.

The May Department Stores Co. reported yesterday that sales in the third quarter of 1979 totaled $667 million, a 7.8 percent gain from 1978's $619 million.

The company earned $19.95 million (88 cents a share), compared with $18.033 million (80 cents) for 1978, a 10 percent increase.

Sales for the nine months were $1.834 billion, up 10.8 percent from 1978. Earnings for the nine months were $43.177 million ($1.91) compared to $35.292 million ($1.57) a year earlier for a 21.7 percent gain.

K mart Corp's. third-quarter sales were up 13.4 percent over the same period last year, Chairman Robert E. Dewar said yesterday.

Sales for the 13 weeks ending Oct. 31 were $3.05 billion, compared with $2.69 billion last year, excluding Australian sales. Earnings per share were 61 cents, up from 54 cents for the same period in 1978, according to Dewar.

Sales for the 39 weeks ended Oct. 31 were $8.71 billion, an increase of 15.1 percent over the same period in 1978, excluding Australian sales. Net income for the first 39 weeks of the year was $212.0 million or $1.69 per share, compared with $183.3 million or $1.47 per share earned in 1978.

Dayton Hudson Corp. reported net earnings rose 30.2 percent in the third quarter of its fiscal year on a revenue hike of 16.9 percent.

The diversified department and specialty store group said net income for the quarter ended Nov. 3 was $29.4 million ($1.23) compared with $24.3 million ($1.03) in the comparable quarter last year.

Revenues rose to $822.4 million from $703.6 million the year before.

For nine months, Dayton Hudson net earnings were $61.8 million, to ($2.60) compared with $37.1 million $1.56) share in 1978. Revenues for the latest nine months totaled $2.21 billion compared with $1.921 billion in the first nine months of fiscal 1978.