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Edge Induced Weightings Of Uniform Hypergraphs And Related Problems, Laars C. Helenius

Dissertations

The starting point of the research is the so called 1-2-3 Conjecture formulated in 2004 by Karoński, Luczak, and Thomason. Roughly speaking it says that the edges of any graph can be weighted from {1, 2, 3} so that the induced vertex coloring (as the sum of weights adjacent to a given vertex) is proper. The conjecture has attracted a lot of interest from researchers over the last decade but is still unanswered. More recently, the conjecture has been studied for hypergraphs.

The main result of this dissertation shows in particular that an analogous conjecture holds for almost all uniform …