## 1 Introduction  
Vehicular ad-hoc networks (VANETs) can provide users a safer and more pleasant driving experience through integrating wireless communication and informatics technologies into the intelligent transportation system (ITS) [1]. However, VANETs face the challenge of frequent connection disruptions due to highly dynamic network topologies, which significantly degrade the network performance [2]. To address this challenge, unmanned aerial vehicles (UAVs) can be considered as the suitable candidates to improve the connectedness of VANETs [3]. For example, UAVs can assist the ground vehicle in data transmission by the \"storage-carry-forward\" (SCF) method, which can effectively improve the message delivery ratio and reduce the end-to-end delay [4]. In UAV-assisted VANETs, UAVs and vehicles are network nodes that transmit messages to each other through multi-hop relays. To fully exploit the advantages of the UAV-assisted VANETs, some relay selection protocols have been proposed in recent years [5; 6; 7; 8; 9; 10; 11; 12]. The works in [5; 6] conceived efficient routing solutions based on the flooding technique to guarantee the robust path and to make the message delivery more reliable. In [7], the problem of relay transmission efficiency was studied by optimizing the transfer probability. Moreover, in our previous work in [8], we formulate the relay selection problem as a multi-objective optimization problem by jointly considering the the state transition probability (STP) of communication interruption and the transmission consumption (TC) including energy consumption and delay consumption. Furthermore, the researchers in [9; 10; 11; 12]analytically derived the probability distribution of the vehicle-to-UAV (V2U) packet end-to-end delay, and used UAVs collaborative communication to decrease the V2U packet delay. The above works have enhanced the communication capability of UAV-assisted VANETs, nevertheless, there are still some problems to be further investigated. Specifically, the authors in [5; 6; 7; 8] improve the data delivery process by designing the routing strategy for the relay selection, but they assume that the link between the source node (SN) and the relay node (RN) is ideal. Although the works in [9; 10; 11; 12] consider the link quality of service (LQoS), they do not take into account the node forward capacity (NFC), which has an important effect on the message delivery ratio and the average end-to-end delay. Moreover, all works in [5; 6; 7; 8; 9; 10; 11; 12] neglect the optimization of the overhead, which is a significant factor that affects whether the relay selection can be successfully executed in practice. Motivated by the above, we investigate the relay selection problem for UAV-assisted VANETs by jointly considering the LQoS and the NFC. Specifically, the LQoS is the ratio of the channel capacity to the delay, which reflects the reliability and stability of the link from the SN to the neighbor node. The NFC represents the delivery probability of the message from the neighbor node to the destination node (DN), which consists of the node activity (NA) and the node encounter frequency (NEF). The main contributions are summarized as follows. * We formulate the relay selection problem as a multi-objective optimization problem. For the considered problem, we first model and analyze the LQoS from the SN to the neighbor node and the NFC from the neighbor node to the DN. Then, we decompose the primal problem into two subproblems and solve them by the graphical method. * Considering the high mobility and cooperative data sharing of UAVs, we propose a relay selection protocol named LQFC with the SCF method. Furthermore, we jointly consider the NEF and the message time-to-live (TTL) to define a utility function to delete redundant copies. The simulation results indicate that our proposed protocol achieves significant performance superiority as compared with other schemes in terms of the message delivery ratio, the average end-to-end delay, and the overhead.