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  1. Context. The role of large-scale magnetic fields in the evolution of star-forming regions remains elusive. Its investigation requires the observational characterization of well-constrained molecular clouds. The Monoceros OB 1 molecular cloud is a large complex containing several structures that have been shown to be engaged in an active interaction and to have a rich star formation history. However, the magnetic fields in this region have only been studied on small scales. Aims. We study the large-scale magnetic field structure and its interplay with the gas dynamics in the Monoceros OB 1 east molecular cloud. Methods. We combined observations of dust polarized emission from the Planck telescope and CO molecular line emission observations from the Taeduk Radio Astronomy Observatory 14-metre telescope. We calculated the strength of the plane-of-sky magnetic field using a modified Chandrasekhar-Fermi method and estimated the mass-over-flux ratios in different regions of the cloud. We used the comparison of the velocity and intensity gradients of the molecular line observations with the polarimetric observations to trace dynamically active regions. Results. The molecular complex shows an ordered large-scale plane-of-sky magnetic field structure. In the northern part, it is mostly orientated along the filamentary structures, while the southern part shows at least two regions with distinct magnetic field orientations. Our analysis reveals a shock region in the northern part right between two filamentary clouds that, in previous studies, were suggested to be involved in a collision. The magnetic properties of the north-main and north-eastern filaments suggest that these filaments once formed a single one, and that the magnetic field evolved together with the material and did not undergo major changes during the evolution of the cloud. In the southern part, we find that either the magnetic field guides the accretion of interstellar matter towards the cloud or it is dragged by the matter falling towards the main cloud. Conclusions. The large-scale magnetic field in the Monoceros OB 1 east molecular cloud is tightly connected to the global structure of the complex. In the northern part, it seems to serve a dynamically important role by possibly providing support against gravity in the direction perpendicular to the field and to the filament. In the southern part, it is probably the most influential factor governing the morphological structure by guiding possible gas inflow. A study of the whole Monoceros OB 1 molecular complex at large scales is necessary to form a global picture of the formation and evolution of the Monoceros OB 1 east cloud and the role of the magnetic field in this process. 
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