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