Selectorless graphite-based resistive random-access memory (RRAM) has been demonstrated by utilizing the intrinsic nonlinear resistive switching (RS) characteristics, without an additional selector or transistor for low-power RRAM array application. The low effective dielectric constant value (k) layer of graphite or graphite oxide is utilized, which is beneficial in suppressing sneak-path currents in the crossbar RRAM array. The tail-bits with low nonlinearity can be manipulated by the positive voltage pulse, which in turn can alleviate variability and reliability issues. Our results provide additional insights for built-in nonlinearity in 1R-only selectorless RRAMs, which are applicable to the low-power memory array, ultrahigh density storage, and in-memory neuromorphic computational configurations.