Handicap Labelings of 4-Regular Graphs
Petr Kovar, Michal Kravcenko, Matej Krbecek, Adam Silber
DOI: 10.15598/aeee.v15i2.2263
Abstract
Let G be a simple graph, let f : V (G) → {1, 2, . . . , |V (G)|} be a bijective mapping. The weight of v ∈ V (G) is the sum of labels of all vertices adjacent to v. We say that f is a distance magic labeling of G if the weight of every vertex is the same constant k and we say that f is a handicap magic labeling of G if the weight of every vertex v is `+f(v) for some constant `. Graphs that allow such labelings are called distance magic or handicap, respectively. Distance magic and handicap labelings of regular graphs are used for scheduling incomplete tournaments. While distance magic labelings correspond to so called equalized tournaments, handicap labelings can be used to schedule incomplete tournaments that are more challenging to stronger teams or players, hence they increase competition and yield attractive schemes in which every game counts. We summarize known results on distance magic and handicap labelings and construct a new infinite class of 4-regular handicap graphs.