22 citations · 36 across the 3 of their papers we have counts for
7 papers
A Solution to the 1-2-3 Conjecture
Ralph Keusch
We show that for every graph without isolated edge, the edges can be assigned weights from {1,2,3} so that no two neighbors receive the same sum of incident edge weights. This solv…
Vertex-coloring graphs with 4-edge-weightings
Ralph Keusch
An edge-weighting of a graph is called vertex-coloring if the weighted degrees yield a proper vertex coloring of the graph. It is conjectured that for every graph without isolated…
A new upper bound on the game chromatic index of graphs
Ralph Keusch
We study the two-player game where Maker and Breaker alternately color the edges of a given graph with colors such that adjacent edges never get the same color. Maker's goa…
Greedy Routing and the Algorithmic Small-World Phenomenom
Karl Bringmann, Ralph Keusch, Johannes Lengler +2
The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However,…
Colorability Saturation Games
Ralph Keusch
We consider the following two-player game: Maxi and Mini start with the empty graph on vertices and take turns, always adding one additional edge to the graph such that the chr…
Average Distance in a General Class of Scale-Free Networks with Underlying Geometry
Karl Bringmann, Ralph Keusch, Johannes Lengler
In Chung-Lu random graphs, a classic model for real-world networks, each vertex is equipped with a weight drawn from a power-law distribution, and two vertices form an edge indepen…