24 citations · 36 across the 11 of their papers we have counts for
14 papers
A Generalization of the Graph Packing Theorems of Sauer-Spencer and Brandt
Hemanshu Kaul, Benjamin Reiniger
We prove a common generalization of the celebrated Sauer-Spencer packing theorem and a theorem of Brandt concerning finding a copy of a tree inside a graph. This proof leads to the…
A Simple Characterization of Proportionally 2-choosable Graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer +1
We recently introduced proportional choosability, a new list analogue of equitable coloring. Like equitable coloring, and unlike list equitable coloring (a.k.a. equitable choosabil…
Proportional Choosability: A New List Analogue of Equitable Coloring
Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer +1
In 2003, Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. In this paper, we motivate and define a new list analogue of…
Subhypergraphs in non-uniform random hypergraphs
Megan Dewar, John Healy, Xavier Pérez-Giménez +4
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph proble…
The Saturation Number of Induced Subposets of the Boolean Lattice
Michael Ferrara, Bill Kay, Lucas Kramer +4
Given a poset , a family of elements in the Boolean lattice is said to be -saturated if (1) contains no copy of as a subposet and (2) every proper superset of …
The game of Overprescribed Cops and Robbers played on graphs
Anthony Bonato, Xavier Pérez-Giménez, Paweł Prałat +1
We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capt…
Perfect matchings and Hamiltonian cycles in the preferential attachment model
Alan Frieze, Xavier Pérez-Giménez, Paweł Prałat +1
In this paper, we study the existence of perfect matchings and Hamiltonian cycles in the preferential attachment model. In this model, vertices are added to the graph one by one, a…
Dynamic coloring parameters for graphs with given genus
Sarah Loeb, Thomas Mahoney, Benjamin Reiniger +1
A proper vertex coloring of a graph is -dynamic if for each , at least colors appear in . In this paper we investigate -dynamic versio…
Chvátal-type results for degree sequence Ramsey numbers
Christopher Cox, Michael Ferrara, Ryan M. Martin +1
A sequence of nonnegative integers is graphic if there is a (simple) graph of order having degree sequence . In this case, is said to realize o…
Coloring, sparseness, and girth
Noga Alon, Alexandr Kostochka, Benjamin Reiniger +2
An -augmented tree is a rooted tree plus edges added from each leaf to ancestors. For , we construct a bipartite -augmented complete -ary tree havi…
The Game Saturation Number of a Graph
James M. Carraher, William B. Kinnersley, Benjamin Reiniger +1
Given a family and a host graph , a graph is -saturated relative to if no subgraph of lies in but adding any e…
Large subposets with small dimension
Benjamin Reiniger, Elyse Yeager
Dorais asked for the maximum guaranteed size of a dimension subposet of an -element poset. A lower bound of order was found by Goodwillie. We provide a sublinear…
A note on list-coloring powers of graphs
Nicholas Kosar, Sarka Petrickova, Benjamin Reiniger +1
Recently, Kim and Park have found an infinite family of graphs whose squares are not chromatic-choosable. Xuding Zhu asked whether there is some such that all th power graph…
A symplectic proof of a theorem of Franks
Brian Collier, Ely Kerman, Benjamin M. Reiniger +2
A celebrated theorem in two-dimensional dynamics due to John Franks asserts that every area preserving homeomorphism of the sphere has either two or infinitely many periodic points…