From the 1 of 15 linked papers with an AI index.
15 papers
Supersaturation for Hypergraph-Weighted Independent Sets
Sam Spiro
The paper develops supersaturation theorems for independent sets in a hypergraph whose size is measured by the number of edges they induce in another hypergraph, and applies these…
On a clique-building game of ErdÅs
Alexandru Malekshahian, Sam Spiro
The following game was introduced in a list of open problems from 1983 attributed to ErdÅs: two players take turns claiming edges of a until all edges are exhausted. Player…
Helly Theorems for Generalized Turán Problems
Sean English, Sam Spiro
Given a graph and a family of graphs , the generalized Turán number is the maximum number of copies of in an -vertex $\mathc…
Random Turán Problems for Graphs with a Vertex Complete to One Part
Sean Longbrake, Sam Spiro
Given a graph , the random Turán problem asks to determine the maximum number of edges in an -free subgraph of . Prior to this work, the only bipartite graphs w…
Metric Dimensions of March Madness Brackets
Sam Spiro
Say you and some friends decide to make brackets for March Madness and are told how each of your brackets scored. The question we ask is: when can you determine how the actual tour…
Tree Posets: Supersaturation, Enumeration, and Randomness
Tao Jiang, Sean Longbrake, Sam Spiro +1
We develop a powerful tool for embedding any tree poset of height in the Boolean lattice which allows us to solve several open problems in the area. We show that: * If …