4 citations · 9 across the 32 of their papers we have counts for
39 papers
Covering Families for DP-Coloring of Cartesian Products with Complete Bipartite Graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Emily A. Psyhogios +3
A famous folklore result in list coloring demonstrating that the gap between the list chromatic number and chromatic number of a graph can be arbitrarily large is: $χ_{\ell}(K_{l,t…
The DP Color Function of Bipartite Graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Gunjan Sharma +1
DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in 2015. As the analogue of $…
The unlabeled list color function of disconnected graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Armin Straub
Given a graph , its chromatic polynomial counts proper -colorings, while the corresponding list color function counts the minimum number of prope…
List Coloring the Cartesian Product of a Complete Graph and Complete Bipartite Graph
Hemanshu Kaul, Leonardo Marciaga, Jeffrey A. Mudrock
We study the list chromatic number of the Cartesian product of a complete graph of order and a complete bipartite graph with partite sets of size and , denoted $χ_{\ell}…
On the DP-chromatic Number of Cartesian Products of Critical Graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Gunjan Sharma
DP-coloring (also called correspondence coloring) is a well-studied generalization of list coloring introduced by Dvořák and Postle in 2015. The following sharp bound on the DP-chr…
A Spectral Turán Problem for a Fixed Tree
Dheer Noal Desai, Hemanshu Kaul, Bahareh Kudarzi
We study the spectral Turán problem for trees. To avoid limiting our perspective to specific families of trees, we parametrize trees in terms of their unique bipartition. We say $T…
Shameful Inequalities for List and DP Coloring of Graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Gunjan Sharma
The chromatic polynomial of a graph is an important notion in algebraic combinatorics that was introduced by Birkhoff in 1912; denoted , it equals the number of proper -…
Counting List Colorings of Unlabeled Graphs
Hemanshu Kaul, Jeffrey A. Mudrock
The classic enumerative functions for counting colorings of a graph , such as the chromatic polynomial , do so under the assumption that the given graph is labeled. In 1…
On strongly and robustly critical graphs
Anton Bernshteyn, Hemanshu Kaul, Jeffrey A. Mudrock +1
In extremal combinatorics, it is common to focus on structures that are minimal with respect to a certain property. In particular, critical and list-critical graphs occupy a promin…
Counting Packings of List-colorings of Graphs
Hemanshu Kaul, Jeffrey A. Mudrock
Given a list assignment for a graph, list packing asks for the existence of multiple pairwise disjoint list colorings of the graph. Several papers have recently appeared that study…
A Polynomial Method for Counting Colorings of Sparse Graphs
Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
The notion of -labeling of graphs, where is a subset of a symmetric group, was introduced in 2019 by Jin, Wong, and Zhu. This notion provides the framework for a common gene…
DP-Coloring of Graphs from Random Covers
Anton Bernshteyn, Daniel Dominik, Hemanshu Kaul +1
DP-coloring (also called correspondence coloring) of graphs is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in .…
An Improved Algorithm for Finding Maximum Outerplanar Subgraphs
Gruia Calinescu, Hemanshu Kaul, Bahareh Kudarzi
We study the NP-complete Maximum Outerplanar Subgraph problem. The previous best known approximation ratio for this problem is 2/3. We propose a new approximation algorithm which i…
An Algebraic Approach for Counting DP-3-colorings of Sparse Graphs
Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in 2015. As the analogue of t…
Flexible list colorings: Maximizing the number of requests satisfied
Hemanshu Kaul, Rogers Mathew, Jeffrey A. Mudrock +1
Flexible list coloring was introduced by Dvořák, Norin, and Postle in 2019. Suppose , is a graph, is a list assignment for , and is a function with n…
Bounding the List Color Function Threshold from Above
Hemanshu Kaul, Akash Kumar, Andrew Liu +5
The chromatic polynomial of a graph , denoted , is equal to the number of proper -colorings of for each . In 1990, Kostochka and Sidorenko intro…
On the List Color Function Threshold
Hemanshu Kaul, Akash Kumar, Jeffrey A. Mudrock +3
The chromatic polynomial of a graph , denoted , is equal to the number of proper -colorings of . The list color function of graph , denoted , is…
The DP Color Function of Clique-Gluings of Graphs
Hemanshu Kaul, Michael Maxfield, Jeffrey A. Mudrock +1
DP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent years after its introduction by Dvořák and Postle in 2…
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…
Non-chromatic-adherence of the DP Color Function via Generalized Theta Graphs
Manh Vu Bui, Hemanshu Kaul, Michael Maxfield +3
DP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent years after its introduction by Dvořák and Postle in 2…
DP-Coloring Cartesian Products of Graphs
Hemanshu Kaul, Jeffrey A. Mudrock, Gunjan Sharma +1
DP-coloring (also called correspondence coloring) is a generalization of list coloring introduced by Dvořák and Postle in 2015. Motivated by results related to list coloring Cartes…
Longitudinal Network Models and Permutation-Uniform Markov Chains
William K. Schwartz, Sonja Petrović, Hemanshu Kaul
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their jo…
A public transit network optimization model for equitable access to social services
Adam Rumpf, Hemanshu Kaul
We present a flexible public transit network design model which optimizes a social access objective while guaranteeing that the system's costs and transit times remain within a pre…
The DP Color Function of Joins and Vertex-Gluings of Graphs
Jack Becker, Jade Hewitt, Hemanshu Kaul +5
DP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent years after its introduction by Dvořák and Postle in 2…