[2] In his dissertation he introduced what is now called the Errera graph,[3] which is a counterexample to the validity of the alleged proof of the four color theorem by Alfred Kempe.
He did research on topology, especially the theory of polyhedra and the Jordan curve theorem.
During World War I, he worked on the acoustic source localization of artillery fire and from 1921 to 1938 taught courses on this subject at the Royal Military Academy.
Errera was an Invited Speaker at the International Congress of Mathematicians in 1924 in Toronto, in 1932 in Zürich, and in 1936 in Oslo.
In 1935 he gave a talk at the inaugural Congrés International des Récréations Mathématiques in Brussels.