Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, November 13, 2014, 12:15 pm

Duration: 45 minutes

Location: OAT S15/S16/S17

Speaker: Pál András Papp

5-edge-weight vertex colorings

A weighting of the edges of a graph induces a coloring of the vertices if we consider the color of a vertex to be the sum of weights on the edges incident to it. A graph is said to be colorable with weights {1, 2, ..., k} if there exists a weighting of the edges with these weights such that the resulting coloring is proper. A series of recent papers address the topic of finding the smallest value k such that every nontrivial graph can be colored with the weights {1, 2, ..., k}, improving the bound towards the conjecture of Karońsky, Łuczak and Thomason, which states that such a coloring is always possible with only the weights {1, 2, 3}. Currently, the best known result is that of Kalkowski, Karońsky and Pfender, giving a surprisingly simple proof for the case of k=5.

Based on the paper "Vertex-Coloring Edge-Weightings: Towards the 1-2-3-Conjecture" by M. Kalkowski, M. Karońsky & F. Pfender.

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