▪ John Jacob Kolodzey (b: 1896) named his mother as "Maria Piccar [or Pekar]" on his marriage record to Alice Brecht in 1919.     
▪ Maria 'Irma' Pekar named her father as "Johann Becker" and her mother as  "Kath. Jabrocki" on her marriage record.
▪ A  baptism record was found for Maria with parents listed as Joannes Pekar  and Catharina Jabroczky dated 13 Oct 1872. This is likely her baptism  record - as it matches the correct time frame and correct parents. No  other records that match both parent names and year of birth have been  found.     
▪ The baptism occurred in Markusovce, but the family was listed as living in Babina 66 (not Markusfalu, or Markusovce). There is a far away town of  Babina, but since this address shows up in multiple baptism and marriage records in Markusovce, it is unlikely that multiple families with the  same address would travel 80 miles across two mountain ranges just to baptize their child in Markusovce.     
▪ Given the above argument, "Babina" is likely the name of a road or a nearby village that has since changed its name. The changing of town names  happened several times in the 18th, 19th, and 20th centuries as different factions ruled over the Slovaks, so this is not uncommon.  
        UPDATE - an old Hungarian map shows the village of Felso Babina southwest of Markusovce.... see the picture in the gallery below.
▪ A search of records for either "Pekar" or "Jabroczky" in the Markusovce records reveals there are no other instances of either family there.  Add to that the fact that the godparents often chose the location for  the baptism, and not the parents, and determining their origin becomes  even harder.     
▪ There  are, however, a large number of Pekar families in the village of Plavec  nad Popradom, and a sizeable number of Jabroczky families in Havka -  both are a short distance from Stara Lubovna.     
▪ Maria married Franciscus Kolodzey in New Jersey, so they may not have known each other in Slovakia.