B. Toft

activity

20082025

collaborators

7 papers

math.CO2025

2-Factors in Graphs

Jan van den Heuvel, Bjarne Toft

An account of 2-factors in graphs and their history is presented. We give a direct graph-theoretic proof of the 2-Factor Theorem and a new variant of it, and also a new complete ch…

math.CO2025

The Tournament Theorem of Rédei revisited

Thomas Schweser, Michael Stiebitz, Bjarne Toft

In 1934 L. Rédei published his famous theorem that the number of Hamiltonian paths in a tournament is odd. In fact it is a corollary of a stronger theorem in his paper. Stronger th…

math.CO2018

Coloring hypergraphs of low connectivity

Thomas Schweser, Michael Stiebitz, Bjarne Toft

For a hypergraph $G$ , let $χ (G), Δ (G),$ and $λ (G)$ denote the chromatic number, the maximum degree, and the maximum local edge connectivity of $G$ , respectively. A result of Rhys P…

math.CO2018

Cut-edges and regular factors in regular graphs of odd degree

Alexander V. Kostochka, André Raspaud, Bjarne Toft +2

We study $2 k$ -factors in $(2 r + 1)$ -regular graphs. Hanson, Loten, and Toft proved that every $(2 r + 1)$ -regular graph with at most $2 r$ cut-edges has a $2$ -factor. We generalize their…

math.CO2016

A Brooks type theorem for the maximum local edge connectivity

Michael Stiebitz, Bjarne Toft

For a graph $G$ , let $\cn(G)$ and $\la(G)$ denote the chromatic number of $G$ and the maximum local edge connectivity of $G$ , respectively. A result of Dirac \cite{Dirac53} implies…

math.CO2008

Double-critical graphs and complete minors

Ken-ichi Kawarabayashi, Anders Sune Pedersen, Bjarne Toft

A connected $k$ -chromatic graph $G$ is double-critical if for all edges $uv$ of $G$ the graph $G - u - v$ is $(k - 2)$ -colourable. The only known double-critical $k$ -chromatic graph…