activity
20102026
most citedMinimum ranks of sign patterns via sign vectors and duality

3 citations · 4 across the 7 of their papers we have counts for

collaborators

10 papers

math.CO2026

High-chromatic tournament parts without a complete pair of cyclic triangles

Guantao Chen, Hein van der Holst, Shengze Wang

Nguyen, Scott, and Seymour conjectured that any two disjoint subtournaments of sufficiently large chromatic number contain cyclic triangles, one in each subtournament, with all edg…

math.CO2026

On the Spectra of Chromatic Number and Chromatic Index of Cyclic Covers

Guantao Chen, Hein van der Holst, Rong Luo +1

For a fixed integer , we study what values of chromatic index and chromatic number can be attained by some -fold cyclic cover of a loopless multigraph. For edge-c…

math.CO2025

Strong binding numbers and factors

Guantao Chen, Mikhail Lavrov, Yuying Ma +2

Let be a simple graph. The -th neighborhood of a vertex subset , denoted , is the set of vertices that are adjacent to at least vertices in …

math.CO2024

The inverse eigenvalue problem for probe graphs

Emelie Curl, Jürgen Kritschgau, Carolyn Reinhart +1

In this paper, we initiate the study of the inverse eigenvalue problem for probe graphs. A probe graph is a graph whose vertices are partitioned into probe vertices and non-probe v…

math.CO2022★ 1 cited

Sparsity of Graphs that Allow Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +5

The parameter of a graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . It is shown that the minimum number of edg…

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 , where is a graph (in which parallel edges are permitted, but loops are not) with and . The edges in …

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 , where is a graph (in which parallel edges and loops are permitted) with and . The edges in 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 . The minimum rank of a sign pattern matrix 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 . If is an sign pattern matrix, the qualitative class of , denoted , is the set…

math.CO2010

Zero forcing parameters and minimum rank problems

Francesco Barioli, Wayne Barrett, Shaun M. Fallat +5

The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity / minimum rank of the family of symme…