21 citations · 43 across the 10 of their papers we have counts for
12 papers
A localized approach to generalized Turán problems
Rachel Kirsch, JD Nir
Generalized Turán problems ask for the maximum number of copies of a graph in an -vertex, -free graph, denoted by ex. We show how to extend the new, localized ap…
Graph Universal Cycles: Compression and Connections to Universal Cycles
Rachel Kirsch, Clare Sibley, Elizabeth Sprangel
Universal cycles, such as De Bruijn cycles, are cyclic sequences of symbols that represent every combinatorial object from some family exactly once as a consecutive subsequence. Gr…
Many cliques in bounded-degree hypergraphs
Rachel Kirsch, Jamie Radcliffe
Recently Chase determined the maximum possible number of cliques of size in a graph on vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the…
Shortened universal cycles for permutations
Rachel Kirsch, Bernard Lidický, Clare Sibley +1
Kitaev, Potapov, and Vajnovszki [On shortening u-cycles and u-words for permutations, Discrete Appl. Math, 2019] described how to shorten universal words for permutations, to lengt…
The tripartite-circle crossing number of graphs with two small partition classes
Charles Camacho, Silvia Fernández-Merchant, Marija Jelić Milutinović +4
A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not…
Many cliques with few edges
Rachel Kirsch, A. J. Radcliffe
Recently Cutler and Radcliffe proved that the graph on vertices with maximum degree at most having the most cliques is a disjoint union of cliques…
Bounding the tripartite-circle crossing number of complete tripartite graphs
Charles Camacho, Silvia Fernández-Merchant, Marija Jelić Milutinović +4
A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not…
The zero forcing polynomial of a graph
Kirk Boyer, Boris Brimkov, Sean English +5
Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to beco…
Maximizing the density of 's in graphs of bounded degree and clique number
R. Kirsch, A. J. Radcliffe
Zykov showed in 1949 that among graphs on vertices with clique number , the Turán graph maximizes not only the number of edges but also the number of copie…
-Foldability of Words
Beth Bjorkman, Garner Cochran, Wei Gao +6
We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word…
Many Triangles with Few Edges
R. Kirsch, A. J. Radcliffe
Extremal problems concerning the number of independent sets or complete subgraphs in a graph have been well studied in recent years. Cutler and Radcliffe proved that among graphs w…
Universal Partial Words over Non-Binary Alphabets
Bennet Goeckner, Corbin Groothuis, Cyrus Hettle +4
Chen, Kitaev, Mütze, and Sun recently introduced the notion of universal partial words, a generalization of universal words and de Bruijn sequences. Universal partial words allow f…