Eric Sullivan
University of Colorado Denver
9 Papers
27 Citations
Eric Sullivan is an academic researcher from University of Colorado Denver. The author has contributed to research in topics: Edge coloring & Planar graph. The author has an hindex of 3, co-authored 9 publications. Previous affiliations of Eric Sullivan include Iowa State University.
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Papers
On the Strong Chromatic Index of Sparse Graphs
Philip DeOrsey,Jennifer Diemunsch,Michael Ferrara,Nathan Graber,Stephen G. Hartke,Sogol Jahanbekam,Bernard Lidicky,Luke L. Nelsen,Derrick Stolee,Eric Sullivan +9 more
TL;DR: The discharging method, the Combinatorial Nullstellensatz, and computation are used to show that if $G$ is a subcubic planar graph with ${\rm girth}(G) \geq 41$ then $\chi'_{s,\ell) \leq 5', answering a question of Borodin and Ivanova and improving a bound from the same paper.
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Saturation of Berge Hypergraphs
TL;DR: In this article, the saturation number of Berge triangles, paths, cycles, stars and matchings in a k-uniform hypergraph is studied, where k is the minimum number of edges in a n-dimensional Berge-F-saturated hypergraph.
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On edge-colored saturation problems
Michael Ferrara,Daniel Johnston,Sarah Loeb,Florian Pfender,Alex Schulte,Heather C. Smith,Eric Sullivan,Michael Tait,Casey Tompkins +8 more
TL;DR: In this paper, the authors considered a variety of colored saturation problems and showed that the extremal graphs can be determined exactly and the order of magnitude for the color saturation function is O(n, \mathcal{C}_2(K_3)) for all edge-colored graphs.
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Saturation Numbers in Tripartite Graphs
Eric Sullivan,Paul S. Wenger +1 more
TL;DR: Saturation numbers of tripartite graphs in tripartites with few edges are studied to determine and exactly and within an additive constant.
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On the Strong Chromatic Index of Sparse Graphs
Philip DeOrsey,Jennifer Diemunsch,Michael Ferrara,Nathan Graber,Stephen G. Hartke,Sogol Jahanbekam,Bernard Lidicky,Luke L. Nelsen,Derrick Stolee,Eric Sullivan +9 more
TL;DR: The strong list chromatic index of a graph is the least number of colors needed to edge-color a graph so that edges at distance at most two receive distinct colors.
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