We introduce and analyze a minimal model of epigenetic silencing in budding yeast, built upon known biomolecular interactions in the system. Doing so, we identify the epigenetic marks essential for the bistability of epigenetic states. The model explicitly incorporates two key chromatin marks, namely H4K16 acetylation and H3K79 methylation, and explores whether the presence of multiple marks lead to a qualitatively different systems behavior. We find that having both modifications is important for the robustness of epigenetic silencing. Besides the silenced and transcriptionally active fate of chromatin, our model leads to a novel state with bivalent (i.e., both active and silencing) marks under certain perturbations (knock-out mutations, inhibition or enhancement of enzymatic activity). The bivalent state appears under several perturbations and is shown to result in patchy silencing. We also show that the titration effect, owing to a limited supply of silencing proteins, can result in counter-intuitive responses. The design principles of the silencing system is systematically investigated and disparate experimental observations are assessed within a single theoretical framework. Specifically, we discuss the behavior of Sir protein recruitment, spreading and stability of silenced regions in commonly-studied mutants (e.g., sas2[Formula: see text], dot1[Formula: see text]) illuminating the controversial role of Dot1 in the systems biology of yeast silencing. 