2 citations · 4 across the 4 of their papers we have counts for
6 papers
Countable ultrahomogeneous graphs on two imprimitive color classes
Sofia Brenner, Irene Heinrich
We classify the countable ultrahomogeneous 2-vertex-colored graphs in which the color classes are imprimitive, i.e., up to complementation they form disjoint unions of cliques. Thi…
Line Planning in Public Transport: Bypassing Line Pool Generation
Irene Heinrich, Philine Schiewe, Constantin Seebach
Line planning, i.e. choosing paths which are operated by one vehicle end-to-end, is an important aspect of public transport planning. While there exists heuristic procedures for ge…
Classification of Finite Highly Regular Vertex-Coloured Graphs
Irene Heinrich, Thomas Schneider, Pascal Schweitzer
A coloured graph is k-ultrahomogeneous if every isomorphism between two induced subgraphs of order at most k extends to an automorphism. A coloured graph is t-tuple regular if the…
Automated Testing and Interactive Construction of Unavoidable Sets for Graph Classes of Small Path-width
Oliver Bachtler, Irene Heinrich
We present an interactive framework that, given a membership test for a graph class and a number , finds and tests unavoidable sets for the class of graphs in $\ma…
2.5-Connectivity: Unique Components, Critical Graphs, and Applications
Irene Heinrich, Till Heller, Eva Schmidt +1
If a biconnected graph stays connected after the removal of an arbitrary vertex and an arbitrary edge, then it is called 2.5-connected. We prove that every biconnected graph has a…
Hajós' cycle conjecture for small graphs
Irene Heinrich, Marco V. Natale, Manuel Streicher
Hajós' conjecture states that an Eulerian graph of order n can be decomposed into at most (n-1)/2 edge-disjoint cycles. We describe preprocessing steps, heuristics and integer prog…