8 citations · 11 across the 14 of their papers we have counts for
14 papers
Pancyclicity of almost-planar graphs
Santiago T. Adams, S. R. Kingan
A non-planar graph is almost-planar if either deleting or contracting any edge makes it planar. A graph with vertices is pancyclic if it contains a cycle of every length from $…
On the epidemic threshold of a network
V. Cherniavskyi, G. Dennis, S. R. Kingan
The graph invariant examined in this paper is the largest eigenvalue of the adjacency matrix of a graph. Previous work demonstrates the tight relationship between this invariant, t…
On cyclically 4-connected cubic graphs
R. J. Kingan, S. R. Kingan
For , let and denote the ladder and Möbius ladder on vertices, respectively. We prove results that build on a result by Wormald that states that any…
Constructing minimally 3-connected graphs
J. P. Costalonga, R. J. Kingan, S. R. Kingan
A -connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the re…
A characterization of 2-neighborhood degree list of diameter 2 graphs
N. Benakli, E. Halleck, S. R. Kingan
Let denote the set of degrees of vertices at distance 2 from . The -neighborhood degree list of a graph is a listing of for every vertex . A degree r…
Deletable edges in 3-connected graphs and their applications
S. R. Kingan
Let and be simple 3-connected graphs such that has an -minor. An edge in is called {\it -deletable} if is 3-connected and has an -minor…
Growth rate of binary matroids with no -minor
S. R. Kingan
We prove that the non-regular binary matroids with no -minor have linear growth rate and the maximum size binary matroids with no -minor are graphic. The main techniq…
Applications of the Strong Splitter Theorem: decomposition results
S. R. Kingan
We use the Strong Splitter Theorem to decompose the excluded minor class of binary matroids with no -minor. Using this theorem we can get the 3-decomposers and the extremal in…
Splitters and Decomposers for Binary Matroids
Sandra Kingan
Let denote the class of binary matroids with no minors isomorphic to . In this paper we give a decomposition theorem for …
On Seymour's Decomposition Theorem
S. R. Kingan
Let be a class of matroids closed under minors and isomorphism. Let be a matroid in with an exact -separation . We say is a -decompo…
A decomposition theorem for binary matroids with no prism minor
Sandra Kingan, Manoel Lemos
The prism graph is the dual of the complete graph on five vertices with an edge deleted, . In this paper we determine the class of binary matroids with no prism mi…
Unlabeled equivalence for matroids representable over finite fields
S. R. Kingan
We present a new type of equivalence for representable matroids that uses the automorphisms of the underlying matroid. Two matrices and representing the same m…
Strong Splitter Theorem
S. R. Kingan, Manoel Lemos
The Splitter Theorem states that, if is a 3-connected proper minor of a 3-connected matroid such that, if is a wheel or whirl then has no larger wheel or whirl, res…
Matroids with at least two regular elements
Sandra Kingan, Manoel Lemos
For a matroid , an element such that both and are regular is called a regular element of . We determine completely the structure of non-regular matr…