Luke L. Nelsen

activity

20142018

most citedOn the Strong Chromatic Index of Sparse Graphs

4 citations · 5 across the 3 of their papers we have counts for

collaborators

4 papers

math.CO2018

Erdős-Szekeres On-Line

Kirk Boyer, Lauren M. Nelsen, Luke L. Nelsen +3

In 1935, Erdős and Szekeres proved that $(m - 1) (k - 1) + 1$ is the minimum number of points in the plane which definitely contain an increasing subset of $m$ points or a decreasing subs…

math.CO2015★ 4 cited

On the Strong Chromatic Index of Sparse Graphs

Philip DeOrsey, Jennifer Diemunsch, Michael Ferrara +7

The strong chromatic index of a graph $G$ , denoted $χ_{s}^{'} (G)$ , is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors.…

math.CO2015★ 1 cited

Color-blind index in graphs of very low degree

Jennifer Diemunsch, Nathan Graber, Lucas Kramer +6

Let $c : E (G) \to [k]$ be an edge-coloring of a graph $G$ , not necessarily proper. For each vertex $v$ , let $c ˉ (v) = (a_{1}, \dots, a_{k})$ , where $a_{i}$ is the number of edges incident…

math.CO2014

Monochromatic cycle partitions of graphs with large minimum degree

Louis DeBiasio, Luke Nelsen

Lehel conjectured that in every $2$ -coloring of the edges of $K_{n}$ , there is a vertex disjoint red and blue cycle which span $V (K_{n})$ . Łuczak, Rödl, and Szemerédi proved Lehel's co…