J. Harant

activity

20172025

most citedLong Cycles and Spanning Subgraphs of Locally Maximal 1-planar Graphs

10 citations · 19 across the 8 of their papers we have counts for

collaborators

10 papers

math.CO2025

Lower bounds on the independence number of a graph in terms of degrees

Jochen Harant, Ingo Schiermeyer

Given an integer $Δ \geq 3$ , let $G_{Δ}$ be the set of connected graphs $G \neq = K_{Δ + 1}$ with maximum degree $Δ$ and, for $i = 1, \dots, Δ$ , let $V_{i} (G)$ be the set of vertices o…

math.CO2025

On the independence number in subcubic graphs

Jochen Harant, Ingo Schiermeyer

For a connected subcubic graph $G \neq = K_{1}$ let $V_{i} (G) = {v \in V (G) ∣ d_{G} (v) = i}$ for $1 \leq i \leq 3.$ Given $c_{1}, c_{2}, c_{3} \in R^{+}$ and $d \in R$ , we sho…

math.CO2022

Minimum Spanning Trees with Bounded Degrees of Vertices in a Specified Stable Set

Christoph Brause, Jochen Harant, Florian Hörsch +1

Given a graph $G$ and sets ${α_{v} ∣ v \in V (G)}$ and ${β_{v} ∣ v \in V (G)}$ of non-negative integers, it is known that the decision problem whether $G$ contains a spanning tree $T…

math.CO2021★ 2 cited

Circumference of essentially 4-connected planar triangulations

Igor Fabrici, Jochen Harant, Samuel Mohr +1

A $3$ -connected graph $G$ is essentially $4$ -connected if, for any $3$ -cut $S \subseteq V (G)$ of $G$ , at most one component of $G - S$ contains at least two vertices. We prove that ev…

math.CO2020

New bounds on domination and independence in graphs

Jochen Harant, Samuel Mohr

We propose new bounds on the domination number and on the independence number of a graph and show that our bounds compare favorably to recent ones. Our bounds are obtained by using…

math.CO2020

Rooted Minors and Locally Spanning Subgraphs

Thomas Böhme, Jochen Harant, Matthias Kriesell +2

Results on the existence of various types of spanning subgraphs of graphs are milestones in structural graph theory and have been diversified in several directions. In the present…

math.CO2019★ 10 cited

Long Cycles and Spanning Subgraphs of Locally Maximal 1-planar Graphs

Igor Fabrici, Jochen Harant, Tomáš Madaras +3

A graph is $1$ -planar if it has a drawing in the plane such that each edge is crossed at most once by another edge. Moreover, if this drawing has the additional property that for e…

math.CO2018

On the Circumference of Essentially 4-connected Planar Graphs

Igor Fabrici, Jochen Harant, Samuel Mohr +1

A planar graph is essentially $4$ -connected if it is 3-connected and every of its 3-separators is the neighborhood of a single vertex. Jackson and Wormald proved that every essenti…

math.CO2017★ 2 cited

Longer Cycles in Essentially 4-Connected Planar Graphs

Igor Fabrici, Jochen Harant, Samuel Mohr +1

A planar 3-connected graph $G$ is called \emph{essentially $4$ -connected} if, for every 3-separator $S$ , at least one of the two components of $G - S$ is an isolated vertex. Jackson…

math.CO2017★ 5 cited

On Selkow's Bound on the Independence Number of Graphs

Jochen Harant, Samuel Mohr

For a graph $G$ with vertex set $V (G)$ and independence number $α (G)$ , S. M. Selkow (Discrete Mathematics, 132(1994)363--365) established the famous lower bound $\sum\limits_{v\in…