3 papers
math.CO2022
On the Domination Order among Elimination Sequences
Michaela Hiller
In 1991, it was shown by Favaron, Mahéo, and Saclé that the residue, which is defined as the number of zeros remaining when the Havel-Hakimi algorithm is applied to a degree sequen…
math.CO2022
Counterexamples to the characterisation of graphs with equal independence and annihilation number
Michaela Hiller
We disprove the characterisation of graphs with equal independence and annihilation number by Larson and Pepper (2011). Series of counterexamples with arbitrary number of vertices,…
math.CO2019
On the Burning Number of -Caterpillars
Michaela Hiller, Eberhard Triesch, Arie M. C. A. Koster
The burning number is a recently introduced graph parameter indicating the spreading speed of content in a graph through its edges. While the conjectured upper bound on the necessa…