WILLIAM HALCOMB OF PERRY COUNTY, AR

I am trying to piece together the Halcomb families of Lawrence, Sharp, Saline, Perry and Pulaski Counties, Arkansas.My great, great, great grandfather was William Halcomb.He was married to Joanna Williams, daughter of Daniel Williams, Sr. of Lebanon, Lawrence, Arkansas.I am trying to determine whothe father was of William Halcomb.I tend to lean toward Caleb Halcomb of Lebanon, Lawrence, Arkansas because he seems to be the oldest, lasting resident of that section.The other two were John Halcomb and Greenham Halcomb but they may have just been passing through.Can anyone help me?