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Full-Text Articles in Physical Sciences and Mathematics
On The Strong Chromatic Index Of Sparse Graphs, Philip Deorsey, Jennifer Diemunsch, Michael Ferrara, Nathan Graber, Stephen Hartke, Sogol Jahanbekam, Bernard Lidicky, Luke Nelsen, Derrick Stolee, Eric Sullivan
On The Strong Chromatic Index Of Sparse Graphs, Philip Deorsey, Jennifer Diemunsch, Michael Ferrara, Nathan Graber, Stephen Hartke, Sogol Jahanbekam, Bernard Lidicky, Luke Nelsen, Derrick Stolee, Eric Sullivan
Faculty Publications
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. The strong list chromatic index, denoted χ′s,ℓ(G), is the least integer k such that if arbitrary lists of size k are assigned to each edge then G can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if G is a subcubic planar graph with girth(G)≥41 then χ′s,ℓ(G)≤5, answering a question …
Additive List Coloring Of Planar Graphs With Given Girth, Axel Brandt, Sogol Jahanbekam, Jennifer Diemunsch
Additive List Coloring Of Planar Graphs With Given Girth, Axel Brandt, Sogol Jahanbekam, Jennifer Diemunsch
Faculty Publications
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two adjacent vertices have distinct sums of labels on their neighbors. The least integer k for which a graph G has an additive coloring is called the additive coloring number of G, denoted \luck(G). Additive coloring is also studied under the names lucky labeling and open distinguishing. In this paper, we improve the current bounds on the additive coloring number for particular classes of graphs by proving results for a list version of additive coloring. We apply the discharging method and …
Weak Dynamic Coloring Of Planar Graphs, Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger
Weak Dynamic Coloring Of Planar Graphs, Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger
Faculty Publications
The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min{k, d(v)} colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.