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In recent years, several close post-common-envelope eclipsing binaries havebeen found to show cyclic eclipse timing variations (ETVs). This effect isusually interpreted either as the gravitational interaction among circumbinarybodies and the host binary -- known as the light travel time (LTT) effect -- oras the quadrupole moment variations in one magnetic active component -- knownas Applegate mechanism. In this study, we present an analysis of the ETV andthe magnetic cycle of the close binary KIC 10544976. This system is composed ofa white dwarf and a red dwarf in a short orbital period (0.35 days) and wasmonitored by ground-based telescopes between 2005 and 2017 and by the Keplersatellite between 2009 and 2013. Using the Kepler data, we derived the magneticcycle of the red dwarf by two ways: the rate and energy of flares and thevariability due to spots. Both methods resulted in a cycle of ~600 days, whichis in agreement with magnetic cycles measured for single low-mass stars. Theorbital period of KIC 10544976 shows only one long-term variation which can befitted by an LTT effect with period of ~16.8 yr. Hence, one possibleexplanation for the ETVs is the presence of a circumbinary body with minimalmass of ~13.4 M_Jup. In the particular scenario of coplanarity between theexternal body and the inner binary, the third body mass is also ~13.4 M_Jup. Inthis case, the circumbinary planet must either have survived the evolution ofthe host binary or have been formed as a consequence of its evolution.

Orbital period variation of KIC 10544976: Applegate mechanism versus light travel time effect