M. Ferrara

activity

20112020

most citedFlexibility of Planar Graphs -- Sharpening the Tools to Get Lists of Size Four

5 citations · 17 across the 12 of their papers we have counts for

collaborators

17 papers

cs.DM2020★ 5 cited

Flexibility of Planar Graphs -- Sharpening the Tools to Get Lists of Size Four

Ilkyoo Choi, Felix Christian Clemen, Michael Ferrara +3

A graph where each vertex $v$ has a list $L (v)$ of available colors is $L$ -colorable if there is a proper coloring such that the color of $v$ is in $L (v)$ for each $v$ . A graph is…

math.CO2018★ 2 cited

Stability of the potential function

Catherine Erbes, Michael Ferrara, Ryan R. Martin +1

A graphic sequence $π$ is potentially $H$ -graphic if there is some realization of $π$ that contains $H$ as a subgraph. The Erdős-Jacobson-Lehel problem asks to determine $σ (H, n)$ ,…

math.CO2017

On Edge-Colored Saturation Problems

Michael Ferrara, Daniel Johnston, Sarah Loeb +6

Let $C$ be a family of edge-colored graphs. A $t$ -edge colored graph $G$ is $(C, t)$ -saturated if $G$ does not contain any graph in $C$ but the additi…

math.CO2017

Navigating Between Packings of Graphic Sequences

Peter L. Erdos, Michael Ferrara, Stephen G. Hartke

Let $π_{1} = (d_{1}^{(1)}, \dots, d_{n}^{(1)})$ and $π_{2} = (d_{1}^{(2)}, \dots, d_{n}^{(2)})$ be graphic sequences. We say they \emph{pack} if there exist edge-disjoint realizations $G_{1}$ and $G_…

math.CO2017

List-Distinguishing Cartesian Products of Cliques

Michael Ferrara, Zoltan Furedi, Sogol Jahanbekam +1

The distinguishing number of a graph $G$ , denoted $D (G)$ , is the minimum number of colors needed to produce a coloring of the vertices of $G$ so that every nontrivial isomorphism i…

math.CO2017

The Saturation Number of Induced Subposets of the Boolean Lattice

Michael Ferrara, Bill Kay, Lucas Kramer +4

Given a poset $P$ , a family $F$ of elements in the Boolean lattice is said to be $P$ -saturated if (1) $F$ contains no copy of $P$ as a subposet and (2) every proper superset of $F$ …

math.CO2016★ 4 cited

Ore and Chvátal-type Degree Conditions for Bootstrap Percolation from Small Sets

Michael Dairyko, Michael Ferrara, Bernard Lidický +3

Bootstrap percolation is a deterministic cellular automaton in which vertices of a graph~ $G$ begin in one of two states, "dormant" or "active". Given a fixed integer $r$ , a dormant…

math.CO2015

Chvátal-type results for degree sequence Ramsey numbers

Christopher Cox, Michael Ferrara, Ryan M. Martin +1

A sequence of nonnegative integers $π = (d_{1}, d_{2}, ..., d_{n})$ is graphic if there is a (simple) graph $G$ of order $n$ having degree sequence $π$ . In this case, $G$ is said to realize o…

math.CO2015

I,F-partitions of Sparse Graphs

Axel Brandt, Michael Ferrara, Mohit Kumbhat +3

A star $k$ -coloring is a proper $k$ -coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-c…

math.CO2015★ 4 cited

On the Strong Chromatic Index of Sparse Graphs

Philip DeOrsey, Jennifer Diemunsch, Michael Ferrara +7

The strong chromatic index of a graph $G$ , denoted $χ_{s}^{'} (G)$ , is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors.…

math.CO2014

Graph Saturation in Multipartite Graphs

Michael Ferrara, Michael S. Jacobson, Florian Pfender +1

Let $G$ be a fixed graph and let $F$ be a family of graphs. A subgraph $J$ of $G$ is $F$ -saturated if no member of $F$ is a subgraph of $J$ , but fo…

math.CO2014

Extending Precolorings to Distinguish Group Actions

Michael Ferrara, Ellen Gethner, Stephen G. Hartke +2

Given a group $Γ$ acting on a set $X$ , a $k$ -coloring $ϕ : X \to {1, \dots, k}$ of $X$ is distinguishing with respect to $Γ$ if the only $γ \in Γ$ that fixes $ϕ$ is the identity action.…

math.CO2014

Partitioning a graph into highly connected subgraphs

Valentin Borozan, Michael Ferrara, Shinya Fujita +4

Given $k \geq 1$ , a $k$ -proper partition of a graph $G$ is a partition $P$ of $V (G)$ such that each part $P$ of $P$ induces a $k$ -connected subgraph of $G$ . We…

math.CO2013

On the approximate shape of degree sequences that are not potentially $H$ -graphic

Catherine Erbes, Michael Ferrara, Ryan R. Martin +1

A sequence of nonnegative integers $π$ is {\it graphic} if it is the degree sequence of some graph $G$ . In this case we say that $G$ is a \textit{realization} of $π$ , and we write…

math.CO2012★ 2 cited

On the Sum Neccesary to Ensure that a Degree Sequence is Potentially H-Graphic

Michael Ferrara, Timothy D. LeSaulnier, Casey K. Moffatt +1

A sequence of nonnegative integers π=(d_1,d_2,...,d_n) is graphic if there is a (simple) graph G with degree sequence π. In this case, G is said to realize or be a realization of π…

math.CO2011

List Distinguishing Parameters of Trees

Michael Ferrara, Ellen Gethner, Stephen G. Hartke +2

A coloring of the vertices of a graph G is said to be distinguishing} provided no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, D…

math.CO2011

Rainbow Matchings of size δ(G) in Properly Edge-colored Graphs

Jennifer Diemunsch, Michael Ferrara, Casey Moffatt +2

A {\it rainbow matching} in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(δ) such that a properly edge-colore…

Flexibility of Planar Graphs -- Sharpening the Tools to Get Lists of Size Four

Stability of the potential function

On Edge-Colored Saturation Problems

Navigating Between Packings of Graphic Sequences

List-Distinguishing Cartesian Products of Cliques

The Saturation Number of Induced Subposets of the Boolean Lattice

Ore and Chvátal-type Degree Conditions for Bootstrap Percolation from Small Sets

Chvátal-type results for degree sequence Ramsey numbers

I,F-partitions of Sparse Graphs

On the Strong Chromatic Index of Sparse Graphs

Graph Saturation in Multipartite Graphs

Extending Precolorings to Distinguish Group Actions

Partitioning a graph into highly connected subgraphs

On the approximate shape of degree sequences that are not potentially H-graphic

On the Sum Neccesary to Ensure that a Degree Sequence is Potentially H-Graphic

List Distinguishing Parameters of Trees

Rainbow Matchings of size δ(G) in Properly Edge-colored Graphs

On the approximate shape of degree sequences that are not potentially $H$ -graphic