We report the discovery of four transiting giant planets around K dwarfs. The planets HATS-47b, HATS-48Ab, HATS-49b, and HATS-72b have masses of $0.369_{-0.021}^{+0.031}$ $M_{J}$, $0.243_{-0.030}^{+0.022}$ $M_{J}$, $0.353_{-0.027}^{+0.038}$ $M_{J}$ and $0.1254pm0.0039$ $M_{J}$, respectively, and radii of $1.117pm0.014$ $R_{J}$, $0.800pm0.015$ $R_{J}$, $0.765pm0.013$ $R_{J}$, and $0.7224pm0.0032$ $R_{J}$, respectively. The planets orbit close to their host stars with orbital periods of $3.9228$ d, $3.1317$ d, $4.1480$ d and $7.3279$ d, respectively. The hosts are main sequence K dwarfs with masses of $0.674_{-0.012}^{+0.016}$ $M_{odot}$, $0.7279pm0.0066$ $M_{odot}$, $0.7133pm0.0075$ $M_{odot}$, and $0.7311pm0.0028$ $M_{odot}$ and with $V$-band magnitudes of $V = 14.829pm0.010$, $14.35pm0.11$, $14.998pm0.040$ and $12.469pm0.010$. The Super-Neptune HATS-72b (a.k.a. WASP-191b and TOI 294.01) was independently identified as a transiting planet candidate by the HATSouth, WASP and TESS surveys, and we present a combined analysis of all of the data gathered by each of these projects (and their follow-up programs). An exceptionally precise mass is measured for HATS-72b thanks to high-precision radial velocity (RV) measurements obtained with VLT/ESPRESSO, FEROS, HARPS and Magellan/PFS. We also incorporate TESS observations of the warm Saturn-hosting systems HATS-47 (a.k.a. TOI 1073.01), HATS-48A and HATS-49. HATS-47 was independently identified as a candidate by the TESS team, while the other two systems were not previously identified from the TESS data. The RV orbital variations are measured for these systems using Magellan/PFS. HATS-48A has a resolved $5.!!^{primeprime}4$ neighbor in Gaia~DR2, which is a common-proper-motion binary star companion to HATS-48A with a mass of $0.22$ $M_{odot}$ and a current projected physical separation of $sim$1,400 au.
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