df <- read.table(text =
"X Y
1 2 3
2 4 5
3 6 7
4 8 9
5 10 11",
header = TRUE)
y_min <- min(df[,"Y"])
# Corresponding X value
x_val_associated <- df[df$Y == y_min, "X"]
x_val_associated
First, you find the Y min using the min function on the "Y" column only. Notice the returned result is just an integer value. Then, to find the associated X value, you can subset the data.frame to only the rows where the minimum Y value is located and extract just the "X" column.
You now have two integer values for X and Y where Y is the min.