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We discuss the possible existence of absolutely stable strange quark matter within three different types of chiral models. We will show that confinement plays a crucial role in determining the conditions for the Bodmer-Witten hypothesis to hold true. We discuss also which are the phenomenological signatures, related to measurements of masses and radii of compact stars, which would prove the existence of strange quark stars.doi:10.1051/epjconf/201713709004 fatcat:wsfbzg5pxjhszlqwk43vbhuo3q