Sulfur-vulcanizable rubber mixture without aromatic process oils, in particular for the tread rubber of vehicle pneumatic tires, containing at least one diene rubber, carbon black, mineral oil plasticizer, and resin. A vehicle pneumatic tire with a tread rubber that is composed at least partially of a rubber mixture of this type vulcanized with sulfur is also disclosed. To improve the chipping and chunking behavior, the rubber mixture can contain at least one diene rubber, 5-100 phr of at least one carbon black with an iodine adsorption number of 100-180 g/kg and a DBP number of 100-150 cm3/100 g, 5-80 phr of at least one mineral oil plasticizer that has a content of polycyclic aromatic compounds determined with the DMSO extract according to the IP 346 method of less than 3% by weight relative to the total weight of the mineral oil plasticizer, and 5-30 phr of at least one resin with an average molecular weight determined with GPC of less than 400 g/mol and a softening point (ring and ball according to ASTM E 28) of less than 40° C.