Exclusive Sum Labellings of Hypergraphs

Christopher Purcell (University of West Bohemia) 

February 24th, 4:00 PM, Innovation E432

Abstract: In this talk we will discuss exclusive sum labellings of graphs, which are well understood, and present some new results extending the notion to hypergraphs. No prior knowledge will be required but basic graph theory will be helpful. For a graph G and a set of positive integers S, an exclusive sum labelling of G is an assignment of positive integers (not in S) to its vertices such that xy is an edge if and only if x+y is in S. The class of graphs with an exclusive sum labelling of size at most k is closed under deleting vertices. These classes are characterised by a universal graph. For hypergraphs the story is more complicated. Our main result is a complete characterisation in terms of minimal forbidden induced subgraphs of the case where k=1, edges have size 3 and vertices have maximum degree 2.