Pneumatic vehicle tyre, having a tread having at least one shoulder-side profile rib which is delimited by a circumferential groove, having a rib inner portion which runs within the ground contact area, a rib outer portion which runs outside the ground contact area, and transverse grooves which terminate at a spacing (a 1) from the shoulder-side circumferential groove, wherein each transverse groove has a first groove wall, a second groove wall lying opposite the latter, and a first and a second groove edge (11, 12); wherein the transverse groove along the first groove edge, contiguous to the first groove wall, has a triangular chamfer-like widening which runs in the rib inner portion and in the rib outer portion and is elongate in the direction of extent of the transverse groove; wherein formed in the rib inner portion is a triangular sloping surface which proceeds from the second groove edge, runs to the second groove wall, and is elongate in the direction of extent of the transverse groove; that the first groove edge is made up of an inner edge portion, a middle edge portion and an outer edge portion, with the middle edge portion forming a first obtuse angle (δ) with the inner edge portion on the side facing away from the transverse groove and forming a second obtuse angle (δ') with the outer edge portion on the side facing the transverse groove, the chamfer-like widening being formed along the outer edge portion and the middle edge portion and having a triangular base lying on the transverse groove, characterized in that the transverse grooves are formed with a maximum width (b QRmax) of 5.0 mm to 9.0 mm, determined in the circumferential direction on the tread periphery, that the outer edge portion is formed so as to run in portions in the rib inner portion and in portions in the rib outer portion; and wherein the triangular sloping surface proceeds from a segment of the second groove edge that forms the triangular base and, together with wall portions (6a, 6b) of the second groove wall, delimits a wedge-shaped projection that is at a spacing from the end of the transverse groove on the inner side of the tread and locally narrows the transverse groove. wherein the transverse groove along the first groove edge, contiguous to the first groove wall, has a triangular chamfer-like widening which runs in the rib inner portion and in the rib outer portion and is elongate in the direction of extent of the transverse groove; wherein formed in the rib inner portion is a triangular sloping surface which proceeds from the second groove edge, runs to the second groove wall, and is elongate in the direction of extent of the transverse groove; that the first groove edge is made up of an inner edge portion, a middle edge portion and an outer edge portion, with the middle edge portion forming a first obtuse angle (δ) with the inner edge portion on the side facing away from the transverse groove and forming a second obtuse angle (δ') with the outer edge portion on the side facing the transverse groove, the chamfer-like widening being formed along the outer edge portion and the middle edge portion and having a triangular base lying on the transverse groove, characterized in that the transverse grooves are formed with a maximum width (b QRmax) of 5.0 mm to 9.0 mm, determined in the circumferential direction on the tread periphery, that the outer edge portion is formed so as to run in portions in the rib inner portion and in portions in the rib outer portion; and wherein the triangular sloping surface proceeds from a segment of the second groove edge that forms the triangular base and, together with wall portions (6a, 6b) of the second groove wall, delimits a wedge-shaped projection that is at a spacing from the end of the transverse groove on the inner side of the tread and locally narrows the transverse groove.