Michael A. Henning

activity

20232026

most citedThe 1/3-conjectures for domination in cubic graphs

1 citations · 1 across the 19 of their papers we have counts for

collaborators

20 papers

math.CO2026

A note on partitioning the vertex set of a graph into a dominating set and a locating dominating set

Dipayan Chakraborty, Florent Foucaud, Michael A. Henning +1

A set $S$ of vertices in a graph $G$ is a dominating set of $G$ if every vertex not in $S$ has a neighbor in $S$ , where two vertices are neighbors if they are adjacent. The dominat…

math.CO2025

A proof of the $\frac{3}{8}$ -conjecture for independent domination in cubic graphs

Boštjan Brešar, Tanja Dravec, Michael A. Henning

A set $S$ of vertices in a graph $G$ is a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in~ $S$ . An independent dominating set in $G$ is a dominating set…

math.CO2025

On the isolation number of graphs with minimum degree four

Wayne Goddard, Michael A. Henning

An isolating set in a graph $G$ is a set $S$ of vertices such that removing $S$ and its neighborhood leaves no edge. The isolation number $ι (G)$ of $G$ (also known as the vertex-ed…

math.CO2025

On $k$ -coalition in graphs: bounds and exact values

Boštjan Brešar, Michael A. Henning, Babak Samadi

Given a graph $G=\big{(}V(G),E(G)\big{)}$, a set $S \subseteq V (G)$ is called a $k$ -dominating set if every vertex in $V (G) ∖ S$ has at least $k$ neighbors in $S$ . Two disjoi…

math.CO2025

Bounds on the game isolation number and exact values for paths and cycles

Csilla Bujtás, Tanja Dravec, Michael A. Henning +1

The isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $X$ is the set of already played vertices, then a vertex can be selected onl…

math.CO2025

On polluted bootstrap percolation in Cartesian grids

Boštjan Brešar, Jaka Hedžet, Michael A. Henning

Given a graph $G$ and assuming that some vertices of $G$ are infected, the $r$ -neighbor bootstrap percolation rule makes an uninfected vertex $v$ infected if $v$ has at least $r$ i…

math.CO2025

Paired domination in trees: A linear algorithm and asymptotic normality

Michael A. Henning, Dimbinaina Ralaivaosaona

A set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ contains a perfect matching (n…

math.CO2025

Paired domination in graphs with minimum degree four

Csilla Bujtás, Michael A. Henning

A set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ admits a perfect matching. The…

math.CO2025

Disjunctive domination in maximal outerplanar graphs

Michael A. Henning, Paras Vinubhai Maniya, Dinabandhu Pradhan

A disjunctive dominating set of a graph $G$ is a set $D \subseteq V (G)$ such that every vertex in $V (G) ∖ D$ has a neighbor in $D$ or has at least two vertices in $D$ at dis…

math.CO2025

Independence, induced subgraphs, and domination in $K_{1, r}$ -free graphs

Yair Caro, Randy Davila, Michael A. Henning +1

Let $G$ be a graph and $F$ a family of graphs. Define $α_{F} (G)$ as the maximum order of any induced subgraph of $G$ that belongs to the family $F$ . F…

math.CO2024

Spreading in claw-free cubic graphs

Boštjan Brešar, Jaka Hedžet, Michael A. Henning

Let $p \in N$ and $q \in N \cup {\infty}$ . We study a dynamic coloring of the vertices of a graph $G$ that starts with an initial subset $S$ of blue…

math.CO2024

An exploration of the balance game

Paul Dorbec, Michael A. Henning, Zsolt Tuza +1

The balance game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of $G$ . Admirable labels the selected vertices b…

math.CO2024

Identifying open codes in trees and 4-cycle-free graphs of given maximum degree

Dipayan Chakraborty, Florent Foucaud, Michael A. Henning

An identifying open code of a graph $G$ is a set $S$ of vertices that is both a separating open code (that is, $N_{G} (u) \cap S \neq = N_{G} (v) \cap S$ for all distinct vertices $u$ and $…

math.CO2024

On total domination subdivision numbers of trees

Michael A. Henning, Jerzy Topp

A set $S$ of vertices in a graph $G$ is a total dominating set of $G$ if every vertex is adjacent to a vertex in $S$ . The total domination number $γ_{t} (G)$ is the minimum cardinalit…

math.CO2024

Best possible upper bounds on the restrained domination number of cubic graphs

Boštjan Brešar, Michael A. Henning

A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex in $V (G) ∖ S$ is adjacent to a vertex in $S$ . A restrained dominating set of $G$ is a domina…

math.CO2024

Identifying codes in triangle-free graphs of bounded maximum degree

Dipayan Chakraborty, Florent Foucaud, Michael A. Henning +1

An identifying code of a closed-twin-free graph $G$ is a set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct, nonempty intersection between their closed ne…

math.CO2024

Identifying codes in graphs of given maximum degree: Characterizing trees

Dipayan Chakraborty, Florent Foucaud, Michael A. Henning +1

An identifying code of a closed-twin-free graph $G$ is a dominating set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct intersection between their closed n…

cs.DM2024★ 1 cited

The 1/3-conjectures for domination in cubic graphs

Paul Dorbec, Michael Antony Henning

A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to a vertex in S . The domination number of G, denoted by $γ$ (G), is the minimum card…

math.CO2023

$k$ -Domination invariants on Kneser graphs

Boštjan Brešar, María Gracia Cornet, Tanja Dravec +1

In this follow-up to [M.G.~Cornet, P.~Torres, arXiv:2308.15603], where the $k$ -tuple domination number and the 2-packing number in Kneser graphs $K (n, r)$ were studied, we are conce…

math.CO2023

Bounds on zero forcing using (upper) total domination and minimum degree

Boštjan Brešar, María Gracia Cornet, Tanja Dravec +1

While a number of bounds are known on the zero forcing number $Z (G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds…

A note on partitioning the vertex set of a graph into a dominating set and a locating dominating set

A proof of the 83​-conjecture for independent domination in cubic graphs

On the isolation number of graphs with minimum degree four

On k-coalition in graphs: bounds and exact values

Bounds on the game isolation number and exact values for paths and cycles

On polluted bootstrap percolation in Cartesian grids

Paired domination in trees: A linear algorithm and asymptotic normality

Paired domination in graphs with minimum degree four

Disjunctive domination in maximal outerplanar graphs

Independence, induced subgraphs, and domination in K1,r​-free graphs

Spreading in claw-free cubic graphs

An exploration of the balance game

Identifying open codes in trees and 4-cycle-free graphs of given maximum degree

On total domination subdivision numbers of trees

Best possible upper bounds on the restrained domination number of cubic graphs

Identifying codes in triangle-free graphs of bounded maximum degree

Identifying codes in graphs of given maximum degree: Characterizing trees

The 1/3-conjectures for domination in cubic graphs

k-Domination invariants on Kneser graphs

Bounds on zero forcing using (upper) total domination and minimum degree

A proof of the $\frac{3}{8}$ -conjecture for independent domination in cubic graphs

On $k$ -coalition in graphs: bounds and exact values

Independence, induced subgraphs, and domination in $K_{1, r}$ -free graphs

$k$ -Domination invariants on Kneser graphs