'nonbipartite' is formed from the negative prefix 'non-' (from Latin 'non' meaning 'not') combined with 'bipartite' (from Latin 'bi-' meaning 'two' + Late Latin/Neo-Latin element 'partitus/partire' meaning 'divided').

'bipartite' arose in Neo-Latin/Modern Latin usage to mean 'divided into two parts' and was adopted into English as 'bipartite'; adding the productive prefix 'non-' produced 'nonbipartite' in technical contexts (notably graph theory).

Originally the components meant 'two' and 'divided into parts'; over time the compound 'bipartite' came to mean 'having two parts' in general and in mathematics/graph theory 'divisible into two vertex classes'; 'nonbipartite' specifically shifted to the technical sense 'not divisible into two such classes', often signaled by the presence of an odd cycle.