On Rosa-type labelings and cyclic graph decompositions - El-Zanati, Saad I.; Eynden, Charles Vanden (Mathematica Slovaca, 2009)
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 2 n +1 while other stricter labelings yielded cyclic G -decompositions of K 2 nx +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.