On Rosa-type labelings and cyclic graph decompositions

Abstract

Abstract A labeling (or valuation) of a graph G is an assignment of integers to the vertices of G subject to certain conditions. A hierarchy of graph labelings was introduced by Rosa in the late 1960s. Rosa showed that certain basic labelings of a graph G with n edges yielded cyclic G-decompositions of K 2n+1 while other stricter labelings yielded cyclic G-decompositions of K 2nx+1 for all natural numbers x. Rosa-type labelings are labelings with applications to cyclic graph decompositions. We survey various Rosa-type labelings and summarize some of the related results.