 Cereceda's conjecture

Cereceda's conjecture is a conjecture in the field of graph theory that pertains to the properties of certain classes of graphs. The conjecture states that for every finite graph \( G \) with at least one edge, the set of all the vertices of \( G \) can be partitioned into a set of vertices of even degree and a set of vertices of odd degree, such that. This partitioning is not trivial and has interesting implications for the structure of the graph.