A5041298817- Advanced Graph Theory Research
- graph theory and CDMA systems
- Advanced Algebra and Logic
- Complexity and Algorithms in Graphs
- Advanced Combinatorial Mathematics
- Graph Labeling and Dimension Problems
- Interconnection Networks and Systems
- semigroups and automata theory
- Graph theory and applications
- Limits and Structures in Graph Theory
- Rough Sets and Fuzzy Logic
- Commutative Algebra and Its Applications
- Advanced Topology and Set Theory
- Computational Geometry and Mesh Generation
- High voltage insulation and dielectric phenomena
- Italian Literature and Culture
- Advanced Optical Network Technologies
- Rings, Modules, and Algebras
- Distributed systems and fault tolerance
- Constraint Satisfaction and Optimization
- Electrostatic Discharge in Electronics
- Polynomial and algebraic computation
- Algebraic structures and combinatorial models
- Lightning and Electromagnetic Phenomena
- Geometric and Algebraic Topology
University of Maryland, College Park
2024
United States Naval Academy
2014-2023
Queen Mary University of London
2022
Pepperdine University
2017
Brunel University of London
2013-2015
Victoria University of Wellington
2011-2013
Louisiana State University
2007-2011
Louisiana State University Agricultural Center
2009
Dielectric materials are foundational to our modern-day communications, defense, and commerce needs. Although dielectric breakdown is a primary cause of failure these systems, we do not fully understand this process. We analyzed the channel propagation dynamics two distinct types electrical trees. One type trees has been formally classified. observed speed tree exceed 10 million meters per second. These results identify substantial gaps in understanding breakdown, filling paramount design...
Matroid theory is often thought of as a generalization graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show that delta-matroids arise the natural extension graphic matroids to setting graphs. various basic ribbon operations concepts have delta-matroid analogues, illustrate how connections can be exploited. Also, in direct analogy with fact The Tutte polynomial matroidal, several polynomials from literature, including Las...
The mutually enriching relationship between graphs and matroids has motivated discoveries in both fields.In this paper, we exploit the similar embedded delta-matroids.There are well-known connections geometric duals of plane matroids.We obtain analogous for various types duality literature surfaces higher genus delta-matroids.Using interplay, establish a rough structure theorem delta-matroids that twists matroids, translate Petrie on ribbon to loop complementation delta-matroids, prove graph...
This technical report accompanies the following three papers. It contains computations necessary to verify some of results claimed in those [1] Carolyn Chun, Deborah Dillon Mayhew, and Stefan H. M. van Zwam. Fan-extensions fragile matroids. In preparation. [2] Geoff Whittle, The structure binary Fano-fragile [3] Ben Clark, {U2,5, U3,5}-fragile
If $\mathcal{S}$ is a set of matroids, then the matroid $M$ $\mathcal{S}$-fragile if, for every element $e\in E(M)$, either $M\backslash e$ or $M/e$ has no minor isomorphic to member $\mathcal{S}$. Excluded-minor characterizations often depend, implicitly explicitly, on understanding classes fragile matroids. In certain cases, when $\mathcal{M}$ minor-closed class and $N\in \mathcal{M}$, only members that contain $N$ as are obtained from by increasing length fans. We prove if this case, we...
Abstract A parallel minor is obtained from a graph by any sequence of edge contractions and deletions. We prove that, for positive integer k , every internally 4‐connected sufficiently high order contains isomorphic to variation K 4, with complete on the vertices degree ‐partition triple fan ‐spoke double wheel, wheel axle, (2k+1)‐rung Möbius zigzag ladder, (2 )‐rung or . also find unavoidable minors 1‐, 2‐, 3‐connected graphs. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 313‐326, 2009
We find the excluded minors for minor-closed class of lattice path polymatroids as a subclass Boolean polymatroids. Like matroids and polymatroids, there are infinitely many minors, but they fall into small number easily-described types.
In her paper "Generalized matroids and supermodular colourings", Tardos studied special delta-matroids obtained from sequences of Higgs lifts; these are the full lift that we treat around which all our results revolve. We give an excluded-minor characterization class within delta-matroids, similar characterizations two other minor-closed classes define using lifts. introduce a minor-closed, dual-closed arise lattice paths. It follows Bouchet can be by removing certain feasible sets; to...
.The natural matroid of an integer polymatroid was introduced to show that a simple construction polymatroids from matroids yields all polymatroids. As we illustrate, the can shed much more light on We focus characterizations using their bases, circuits, and cyclic flats along with rank each flat element; offer some new insights into known characterizations.Keywordsnatural matroidinteger polymatroidbasescircuitscyclic flatsMSC codes05B35