Realizing the chromatic numbers and orders of spinal quadrangulations of surfaces

A method is suggested for construction of quadrangulations of the closed orientable surface with given genus g and either (1) with given chromatic number or (2) with given order allowed by the genus g. In particular, N. Hartsfield and G. Ringel’s results [Minimal quadrangulations of orientable surfaces, J. Combin. Theory, Series B 46 (1989) 84–95] are generalized by way of generating minimal quadrangulations of infinitely many other genera.