9 citations · 50 across the 22 of their papers we have counts for
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Sum-of-Squares Certificates for Vizing's Conjecture via Determining Gröbner Bases
Elisabeth Gaar, Melanie Siebenhofer
The famous open Vizing conjecture claims that the domination number of the Cartesian product graph of two graphs and is at least the product of the domination numbers of $G…
A characterization of graphs with regular distance- graphs
Elisabeth Gaar, Daniel Krenn
For non-negative integers~, we consider graphs in which every vertex has exactly vertices at distance~, i.e., graphs whose distance- graphs are -regular. We call su…
Towards a Computational Proof of Vizing's Conjecture using Semidefinite Programming and Sums-of-Squares
Elisabeth Gaar, Daniel Krenn, Susan Margulies +1
Vizing's conjecture (open since 1968) relates the product of the domination numbers of two graphs to the domination number of their Cartesian product graph. In this paper, we formu…
On -Bend and Monotonic -Bend Edge Intersection Graphs of Paths on a Grid
Eranda Çela, Elisabeth Gaar
If a graph can be represented by means of paths on a grid, such that each vertex of corresponds to one path on the grid and two vertices of are adjacent if and only if…
Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a Grid
Eranda Cela, Elisabeth Gaar
In a representation of a graph as an edge intersection graph of paths on a grid (EPG) every vertex of is represented by a path on a grid and two paths share a grid edge iff…
An Optimization-Based Sum-of-Squares Approach to Vizing's Conjecture
Elisabeth Gaar, Daniel Krenn, Susan Margulies +1
Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formula…