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

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9 papers · 1 filter

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…

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

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