[hal-01184371] Largest cliques in connected supermagic graphs

A graph G=(V,E) is said to be \emphmagic if there exists an integer labeling f: V∪ E →[1, |V∪ E|] such that f(x)+f(y)+f(xy) is constant for all edges xy∈E. Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most 3n^2+o(n^2) which contain a complete graph of order n. Bounds on Sidon sets show that the order of such a graph is at least n^2+o(n^2). We close the gap between those two bounds by showing that, for any given graph H of order n, there are connected magic graphs of order n^2+o(n^2) containing H as an induced subgraph. Moreover it can be required that the graph admits a supermagic labelling f, which satisfies the additional condition f(V)=[1,|V|].

from HAL : Dernières publications http://ift.tt/1DQQO8r