The PXE standard requires the PXE booting client receiving 2 parameters: a TFTP server IP and the NBP name (Network Boot program). This info is either carried within the DHCP offer (if you have the required credentials to configure these parameters in the DHCP server) or in a proxyDHCP server offer otherwise. A proxyDHCP server is defined in the PXE standard and allows to offer PXE parameters in networks where the DHCP infrastructure is only used to provide IPs and related info but no network boot data.
Next the PXE booting client will always try to TFTP retrieve and run the NBP.
PXE needs a TFTP server
DHCP uses MAC and IP broadcast addresses, this traffic is confined within the collision domain (Ethernet stuff) and IP sub-network by routing gear; if your DHCP client needs to contact a DHCP or proxyDHCP server crossing collision domain and/or subnetwork boundaries the corresponding "DHCP relay" or "IP helpers" services must be configured in the affected routing gear