Marina Arav

activity

20122024

most citedMinimum ranks of sign patterns via sign vectors and duality

3 citations · 4 across the 5 of their papers we have counts for

collaborators

7 papers

math.CO2024

The stable maximum nullity of digraphs and $1$ -DAGs

Marina Arav, Hein van der Holst

Given a digraph $D = (V, A)$ with vertex-set $V = {1, \dots, n}$ and arc-set $A$ , we denote by $Q (D)$ the set of all real $n \times n$ matrices $B = [b_{u, w}]$ with $b_{u, u} \neq = 0$ for al…

math.CO2014

Two-connected signed graphs with maximum nullity at most two

Marina Arav, Frank J. Hall, Zhongshan Li +1

A signed graph is a pair $(G, Σ)$ , where $G = (V, E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V = {1, \dots, n}$ and $Σ \subseteq E$ . The edges in $Σ$ …

math.CO2014

On the inertia set of a signed graph with loops

Marina Arav, Hein van der Holst, John Sinkovic

A signed graph is a pair $(G, Σ)$ , where $G = (V, E)$ is a graph (in which parallel edges and loops are permitted) with $V = {1, \dots, n}$ and $Σ \subseteq E$ . The edges in $Σ$ are call…

math.CO2013★ 3 cited

Minimum ranks of sign patterns via sign vectors and duality

Marina Arav, Frank J. Hall, Zhongshan Li +3

A {\it sign pattern matrix} is a matrix whose entries are from the set ${+, -, 0}$ . The minimum rank of a sign pattern matrix $A$ is the minimum of the ranks of the real matrices…

math.CO2013

The minimum rank of a sign pattern matrix with a 1-separation

Marina Arav, Frank J. Hall, Zhongshan Li +3

A sign pattern matrix is a matrix whose entries are from the set ${+, -, 0}$ . If $A$ is an $m \times n$ sign pattern matrix, the qualitative class of $A$ , denoted $Q (A)$ , is the set…

math.CO2012

A graph minors characterization of signed graphs whose signed Colin de Verdière parameter $ν$ is two