This issue especially concerns the reading of Kaddish after Ha-Kvura.
The halacha is clear that we do not say Kaddish with less than 10 males (M. Soferim 10:6, H. Tefillah 8:4-5, Tur and SA OC 55:1). It is no different when holding a funeral. See for instance what R Yaakov Goldstein writes in The laws of customs and mourning, vol 1, ch. 8, section I
Immediately following the completion of the burial [i.e. forming of the mound on the grave, and recital of Tziduk Hadin and Mizmor 49], it is customary [for the male mourners] to recite the specially formulated Kaddish, which includes a stanza of “Asid L’Ischadata Alma” and is thus called by this name. [...] It may only be said if a Minyan is present, as is the rule by any Kaddish.
Similarly R Maurice Lamm writes in The Jewish Way in Death and Mourning, p. 66 (here)
Kaddish is not recited at all when the grave cannot be filled in the presence of a minyan.