SelectedWorks - Dan Slilaty

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Selected Works of Dan Slilaty

Professor, Mathematics and Statistics

Dr. Slilaty completed his Ph.D. in mathematics in 2000 and then spent the following year as a visiting assistant professor at the George Washington University in Washington DC. He came to Wright State in the fall of 2001.

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About Dan Slilaty

Dr. Slilaty completed his Ph.D. in mathematics in 2000 and then spent the following year as a visiting assistant professor at the George Washington University in Washington DC. He came to Wright State in the fall of 2001.

Present	Associate Professor, Wright State University ‐ Mathematics and Statistics
Institution Organization Position Type Position Title Time Period to Options Current Position Affiliate my profile with this Institution

Physical Sciences and Mathematics and Mathematics

Graph Theory and Matroid Theory

Department Page

Math/Microbiology Bldg 113

3640 Colonel Glenn Hwy

Dayton, OH 45435-0001

(937) 775-2572

Email:

Articles (34)

Representations of Signed Graphs

Journal of Algebraic Combinatorics (2023)

Yuqing Chen, Anthony B Evans, Xiaoyu Liu, Daniel Slilaty, et al.

We extend the concept of graph representations modulo integers introduced by Erdös and Evans to graph representations over finite rings ...

On Colorings and Orientations of Signed Graphs

Discrete Mathematics Letters (2023)

A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and ...

Graphs Without a 2C3-Minor and Bicircular Matroids Without a U3 ...

Transactions on Combinatorics (2023)

In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the ...

Odd Solutions to Systems of Inequalities Coming From Regular Chain ...

Discrete Mathematics Letters (2023)

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these ...

Hamilton Cycles in Bidirected Complete Graphs

Contributions to Discrete Mathematics (2022)

Arthur Busch, Mohammed A Mutar and Daniel Slilaty

Zaslavsky observed that the topics of directed cycles in directed graphs and alternating cycles in edge 2-colored graphs have a ...

Matrix Representations of Frame and Lifted-Graphic Matroids Correspond To Gain ...

Journal of Combinatorial Theory, Series B (2022)

Daryl Funk, Irene Pivotto and Daniel Slilaty

Let M be a 3-connected matroid and let F" role="presentation"> be a field. Let A be a matrix over F" ...

Characterization of a Family of Rotationally Symmetric Spherical Quadrangulations

ARS Mathematica Contemporanea (2022)

Lowell Abrams and Daniel Slilaty

A spherical quadrangulation is an embedding of a graph G in the sphere in which each facial boundary walk has ...

Coloring Permutation-Gain Graphs

Contributions to Discrete Mathematics (2021)

Correspondence colorings of graphs were introduced in 2018by Dvoˇr ́ak and Postle as a generalization of list colorings of graphswhich ...

The Family of Bicircular Matroids Closed Under Duality

Vaidy Sivaraman and Daniel Slilaty

We characterize the 3-connected members of the intersection of the class of bicircular and cobi- circular matroids. Aside from some ...

Describing Quasi-Graphic Matroids

European Journal of Combinatorics (2020)

Nathan Bowler, Daryl Funk and Dan Slilaty

The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids ...

The Graphs That Have Antivoltages Using Groups of Small Order

Discrete Mathematics (2019)

Vaidy Sivaraman and Dan Slilaty

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the ...

Bounding and Stabilizing Realizations of Biased Graphs With a Fixed ...

Journal of Combinatorial Theory, Series B (2017)

Nancy Ann Neudauer and Dan Slilaty

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of ...

Flexibility of Projective-Planar Embeddings

Journal of Combinatorial Theory, Series B (2017)

John Maharry, Neil Robertson, Vaidy Sivaraman and Dan Slilaty

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of ...

Projective-planar graphs with no K3,4-minor. II.

Journal of Graph Theory (2016)

John Maharry and Dan Slilaty

The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also ...

Bicircular Matroids Representable over GF(4) or GF(5)

Discrete Mathematics (2016)

Deborah Chun, Tyler Moss, Dan Slilaty and Xiangqian Zhou

Given a bicircular matroid B(G) and q∈{4,5}, we characterize when the bicircular matroid B(G) is GF(q)-representable by precisely describing the ...

Clones in 3-Connected Frame Matroids

Discrete Mathematics (2016)

Jakayla Robbins, Dan Slilaty and Xiangqian Zhou

We determine the structure of clonal classes of 3-connected frame matroids in terms of the structure of biased graphs. Robbins ...

Cellular Automorphisms and Self-Duality

Transactions of the American Mathematical Society (2015)

Lowell Abrams and Dan Slilaty

We catalog up to a type of reducibility all cellular automorphisms of the sphere, projective plane, torus, Klein bottle, and ...

Characterization of Line-Consistent Signed Graphs

Discussiones Mathematicae Graph Theory (2015)

Dan Slilaty and Thomas Zaslavsky

The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle ...

The Minimal Zn-Symmetric Graphs that are Not Zn-Spherical

European Journal of Combinatorics (2015)

Lowell Abrams and Dan Slilaty

Given a graph G equipped with faithful and fixed-point-free Γ-action (Γ a finite group) we define an orbit minor H ...

Unavoidable Minors of Large 4-Connected Bicircular Matroids

Annals of Combinatorics (2015)

Deborah Chun, Tyler Moss, Dan Slilaty and Xiangqian Zhou

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given ...

Some Minor-Closed Classes of Signed Graphs

Discrete Mathematics (2013)

Dan Slilaty and Xiangqian Zhou

We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein ...

Projective-Planar Graphs With No K3,4-Minor

Journal of Graph Theory (2011)

John Maharry and Dan Slilaty

An exact structure is described to classify the projective‐planar graphs that do not contain a K3, 4‐minor.

Integer Functions on the Cycle Space and Edges of a ...

Graphs and Combinatorics (2010)

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of ...

The Regular Excluded Minors for Signed-Graphic Matroids

Combinatorics Probability & Computing (2009)

Hongxun Qin, Dan Slilaty and Xiangqian Zhou

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),...,M*(G29),R15,R16. Here G1,...,G29 ...

Connectivity in Frame Matroids

Discrete Mathematics (2008)

Dan Slilaty and Hongxun Qin

We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame ...