Photometric investigation of the K-type extremely shallow contact binary V1799 Orion

New multi-color light curves of the very short period K-type eclipsing binary V1799 On were obtained and analyzed with the Wilson-Devinney code. The photometric solutions reveal that the system is a W-type shallow-contact binary with a mass ratio of q = 1.335(+/- 0.005) and a degree of contact of about f = 3.5(+/- 1.1)%. In general, the results are in good agreement with what is reported by Samec. Dramatic manifestations of the O'Connell effect that appear in the light curves can be explained well by employing starspots on the binary surface, which confirms that the system is active at present. Several new times of light minimum were obtained. All the available times of light minimum were collected, along with the recalculated and newly obtained values. Applying a least-squares method to the constructed O - C diagram, a new ephemeris is derived for V1799 Ori. The orbital period is found to show a continuous weak increase at a rate of 1.8(+/- 0.6) x 10(-8) d yr(-1). The extremely shallow contact, together with the period increase, suggests that the binary may be at a critical stage predicted by thermal relaxation oscillation theory.