Counterexamples:
Methane is a saturated hydrocarbon and has
four hydrogens bonded to its carbon.
Ethyne, formerly known as
acetylene, is an
unsaturated hydrocarbon, and has just one hydrogen on each carbon, as has the
aromatic compound
benzene.
Naphthalene has less than one hydrogen per carbon.
Isobutane, or
2-methyl-propane, is a fairly common branched saturated hydrocarbon.