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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Showing 2024Show all

8 papers · 1 filter

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…