Recently 5-hydroxymethyl-2'-deoxycytidine (5hmdC), 5-formyl-2'-deoxycytidine (5fdC), and 5-carboxyl-2'-deoxycytidine (5cadC) were discovered in mammalian DNA as oxidation products of 5-methyl-2'-deoxycytidine (5mdC) induced by the ten-eleven translocation family of enzymes. These oxidized derivatives of 5mdC may not only act as intermediates of active cytosine demethylation in mammals but also ...

We prove that a graph G contains no induced 5-vertex path and no induced complement of a 5-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement (where split unification is a new class-preserving operation that is introduced in this paper).