J. Nickel

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math.CO2025

Locally interval graphs are circular-arc graphs

Tara Abrishami, Sandra Albrechtsen, Nathan Bowler +2

Circular-arc graphs are graphs that can be represented as intersection graphs of subpaths of a cycle. Interval graphs are graphs that can be represented as intersection graphs of s…

math.CO2025

A generalisation of Menger's theorem in bidirected graphs

Ebrahim Ghorbani, Jana Katharina Nickel, Florian Reich

Menger's theorem - the maximum number of vertex-disjoint $X$ - $Y$ paths is equal to the minimum size of an $X$ - $Y$ separator - is generally not true in bidirected graphs. We prove t…

math.CO2025

Disjoint $X$ -paths in bidirected graphs

Jana K. Nickel

Let $B$ be a bidirected multigraph with signing $σ$ , let $X$ be a set of vertices in $B$ , and let $k$ be a non-negative integer. For any pair of vertex sets $S, T \subset V (B)$ satis…

Locally interval graphs are circular-arc graphs

A generalisation of Menger's theorem in bidirected graphs

Disjoint X-paths in bidirected graphs

Disjoint $X$ -paths in bidirected graphs