The most energetic solar flares are typically associated with the ejection of a cloud of coronal material into the heliosphere in the form of a coronal mass ejection (CME). However, there exist large flares which are not accompanied by a CME... The existence of these non-eruptive flares raises the question of whether such flares suffer from a lack of access to nearby open fields in the vicinity above the flare (reconnection) site. In this study, we use a sample of 56 flares from Sunspot Cycles 23 and 24 to test whether active regions that produce eruptive X-class flares are preferentially located near coronal magnetic field domains that are open to the heliosphere, as inferred from a potential field source surface model. The study shows that X-class flares having access to open fields are eruptive at a higher rate than those for which access is lacking. The significance of this result should be moderated due to the small number of non-eruptive X-class flares in the sample, based on the associated Bayes factor. (read more)