arXiv subjects

Jagdeep Singh

Publications and source records attributed to Jagdeep Singh.

16 recordsLinked to original sources

arXiv2026

Degeneracy: From Graphs to Matroids

A graph is $k$-degenerate if every subgraph has a vertex of degree at most $k$. We extend this notion to matroids, defining a loopless matroid $M$ to be $k$-degenerate if every restriction of $M$ contains a cocircuit of size at most $k$; $M$ is minimally $k$-degenerate if it has cogirth $k$ and every proper restriction of $M$ has cogirth at most $k-1$. Our main result characterizes extremal minimally $k$-degenerate matroids. We also extend the known arboricity bound for matroids, showing that $k$-degenerate matroids have arboricity at most $k$ and providing sharper bounds.

math.CO↗

arXiv2026

The connected binary matroids with a pair of elements in no non-spanning circuits

Let $M$ be a simple connected binary matroid, and let $e$ and $f$ be distinct elements of $M$. It is well known that, when the only circuits containing $e$ are spanning, $M$ is a circuit with at least three elements. This paper proves that if every circuit containing $\{e,f\}$ is spanning, then the canonical tree decomposition of $M$ is a path in which each vertex is labeled by a circuit, a copy of $U_{1,3}$, or a binary spike having one non-tip element deleted.

math.CO↗

arXiv2025

Structural Bounds and Forbidden Induced Subgraphs for Edge-Add Graph Classes

A class $\mathcal{G}$ of graphs is hereditary if it is closed under taking induced subgraphs. We investigate the edge-add class, $\mathcal{G}^{\mathrm{add}}$, consisting of graphs that can be made members of $\mathcal{G}$ by adding at most one edge. While it is known that the operations of vertex deletion and edge deletion preserve the finiteness of forbidden induced subgraphs for classes with finite exclusions, the behavior of edge addition on classes with infinite exclusions remains largely unexplored. We characterize the edge-add class of chordal graphs by their forbidden induced subgraphs and extend the result to a general finiteness theorem: for any fixed $p\ge0$, the set of forbidden induced subgraphs for $p$-edge-add chordal graphs that are not cycles is finite. In contrast, we show that this phenomenon does not extend to perfect graphs. Furthermore, we provide explicit structural bounds proving that edge addition preserves finiteness for base classes with finitely many exclusions. We conclude by providing the complete structural characterizations and explicit minimal obstruction lists for the edge-add classes of split and threshold graphs, and generalize these results to $(p,q)$-edge split graphs.

math.CO↗

arXiv2025

Loose elements in binary and ternary matroids

We call a matroid element "loose" if it is contained in no circuits of size less than the rank of the matroid. A matroid in which all elements are loose is a paving matroid. Acketa determined all binary paving matroids, while Oxley specified all ternary paving matroids. We characterize the binary matroids that contain a loose element. For ternary matroids with a loose element, we show that their size is linear in terms of their rank. Moreover, for a prime power $q$, we give a partial characterization of $GF(q)$-representable matroids that have two or more loose elements; we note Rajpal's partial characterization of $GF(q)$-representable paving matroids as a consequence.

math.CO↗

arXiv2024

$k$-loose elements and $k$-paving matroids

For a matroid of rank $r$ and a non-negative integer $k$, an element is called $k$-loose if every circuit containing it has size greater than $r-k$. Zaslavsky and the author characterized all binary matroids with a $1$-loose element. In this paper, we establish a sharp linear bound on the size of a binary matroid, in terms of its rank, that contains a $k$-loose element. A matroid is called $k$-paving if all its elements are $k$-loose. Rajpal showed that for a prime power $q$, the rank of a $GF(q)$-matroid that is $k$-paving is bounded. We provide a bound on the rank of $GF(q)$-matroids that are cosimple and have two $k$-loose elements. Consequently, we deduce a bound on the rank of $GF(q)$-matroids that are $k$-paving. Additionally, we provide a bound on the size of binary matroids that are $k$-paving.

math.CO↗

arXiv2024

Extensions and Deletions of matroid classes closed under flats

We call a class of matroids hereditary if it is closed under restriction to flats. For a hereditary class $\mathcal{M}$, its extension class consists of all matroids in $\mathcal{M}$ together with their single-element extensions. The deletion class consists of all matroids in $\mathcal{M}$ along with their single-element deletions. We prove that if $\mathcal{M}$ has finitely many forbidden flats, then the forbidden flats for its extension class have bounded rank. For $GF(q)$-representable matroids where $q$ is in $\{2,3\}$, we exploit correspondence with $2$-colorings of projective geometries to establish the analogous result for the deletion class. We also note the consequences for hereditary classes of graphs, discussing the interplay of graphs and matroids.

math.CO↗

arXiv2024

Edge-apexing in hereditary classes of graphs

A class $\mathcal{G}$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $G^{epex}$ the class of graphs that are at most one edge away from being in $\mathcal{G}$. We note that $G^{epex}$ is hereditary and prove that if a hereditary class $\mathcal{G}$ has finitely many forbidden induced subgraphs, then so does $G^{epex}$. The hereditary class of cographs consists of all graphs $G$ that can be generated from $K_1$ using complementation and disjoint union. Cographs are precisely the graphs that do not have the $4$-vertex path as an induced subgraph. For the class of edge-apex cographs our main result bounds the order of such forbidden induced subgraphs by 8 and finds all of them by computer search.

math.CO↗

arXiv2023

Apex Graphs and Cographs

A class $\mathcal{G}$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $\mathcal{G}^\mathrm{apex}$ the class of graphs $G$ that contain a vertex $v$ such that $G-v$ is in $\mathcal{G}$. We prove that if a hereditary class $\mathcal{G}$ has finitely many forbidden induced subgraphs, then so does $\mathcal{G}^\mathrm{apex}$. The hereditary class of cographs consists of all graphs $G$ that can be generated from $K_1$ using complementation and disjoint union. A graph is an apex cograph if it contains a vertex whose deletion results in a cograph. Cographs are precisely the graphs that do not have the $4$-vertex path as an induced subgraph. Our main result finds all such forbidden induced subgraphs for the class of apex cographs.

math.CO↗

arXiv2023

Detecting and Controlling Smart Lights with LiTalk

The rapid increase in demand for wireless controlled Smart Lighting has created a need to automate the mapping between the identifiers for individual light sources and their physical locations. To control Smart Lights, their IDs and physical locations relative to each other must be determined. Nowadays, skilled technicians perform this process manually, which requires a lot of effort, is time-consuming, and incurs high costs, particularly with non-stationary lights. Visible Light Communication has been presented as a possible solution to this problem. This paper presents an approach based on Visible Light Communication that leverages Machine Learning to automate the mapping process between the identifiers and the relative physical location of Smart Lights. We show that our approach provides a better location-mapping performance compared to existing methods.

eess.SP↗

arXiv2022

Cographs and 1-sums

A graph that can be generated from $K_1$ using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from $K_1$ using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph.

math.CO↗

arXiv2022

Vortex-Stretching based Large Eddy Simulation Framework for Wind Farms

In large wind farms, wake distribution behind a wind turbine causes a considerable reduction of wind velocity for downstream wind turbines, resulting in a significant amount of power loss. Therefore, it is very crucial to predict wind turbine wakes efficiently. Thus, we propose a large-eddy simulation (LES) methodology, which takes the vorticity stretching to model transients in wind turbine wakes. In addition, we present an improved actuator disk model, which accounts for two-way feedback between the atmosphere and the wakes. First, we show that the vertical profile of the mean wind predicted with the new model has an excellent agreement with experimental measurements. Next, we validate the predicted Reynolds stresses against wind tunnel data and show that the dispersive stresses account for about 40% of Reynolds stresses. Finally, we show that the proposed LES method accurately predicts the characteristics of wind turbine wakes. Comparing the LES results with previously reported data, we have found that the new LES framework accurately predicts the flow statistics in both the near-wake and the far-wake regions.

physics.flu-dyn↗

arXiv2022

Dynamic modelling of near-surface turbulence in large eddy simulation of wind farms

In large eddy simulation of atmospheric boundary layer flows over wind farms, wall-layer models are generally imposed for the surface fluxes without considering the spatial variability of the surface roughness. In this study, we consider the near-surface model in conjunction with square of the velocity gradient tensor to model the adaptive dissipation of turbulence production. The surface roughness is incorporated through Monin-Obhukhov similarity theory for the computational cells immediately adjacent to the Earth's surface. The underlying proposed near-surface model captures the significant amount of Reynolds stresses in the near-surface and is able to maintain the log-law profile in wind farms. The present study indicates that the suggested `near-surface model' is relatively robust in comparison to the classical `near-wall model'.

physics.flu-dyn↗

arXiv2022

Generalizing Cographs to 2-Cographs

A graph in which every connected induced subgraph has a disconnected complement is called a cograph. Such graphs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We define a $2$-cograph to be a graph in which the complement of every $2$-connected induced subgraph is not $2$-connected. We show that, like cographs, $2$-cographs can be recursively defined. But, unlike cographs, $2$-cographs are closed under induced minors. We characterize the class of non-$2$-cographs for which every proper induced minor is a $2$-cograph. We further find the finitely many members of this class whose complements are also induced-minor-minimal non-$2$-cographs.

math.CO↗

arXiv2021

Elastic elements in 3-connected matroids

It follows by Bixby's Lemma that if $e$ is an element of a $3$-connected matroid $M$, then either ${\rm co}(M\delete e)$, the cosimplification of $M\delete e$, or ${\rm si}(M/e)$, the simplification of $M/e$, is $3$-connected. A natural question to ask is whether $M$ has an element $e$ such that both ${\rm co}(M\delete e)$ and ${\rm si}(M/e)$ are $3$-connected. Calling such an element "elastic", in this paper we show that if $|E(M)|\ge 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans and, up to duality, $M$ has no $3$-separating set $S$ that is the disjoint union of a rank-$2$ subset and a corank-$2$ subset of $E(M)$ such that $M|S$ is isomorphic to a member or a single-element deletion of a member of a certain family of matroids.

math.CO↗

arXiv2021

The smallest class of binary matroids closed under direct sums and complements

The class of cographs or complement-reducible graphs is the class of graphs that can be generated from $K_1$ using the operations of disjoint union and complementation. By analogy, this paper introduces the class of binary comatroids as the class of matroids that can be generated from the empty matroid using the operations of direct sum and taking complements inside of binary projective space. We show that a proper flat of a binary comatroid is a binary comatroid. Our main result identifies those binary non-comatroids for which every proper flat is a binary comatroid. The paper also proves the corresponding results for ternary matroids.

math.CO↗

arXiv2020

Complementation, Local Complementation, and Switching in Binary Matroids

In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set $V$ can be obtained from a complete graph on $V$ via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. The last operation involves taking the complement in the neighbourhood of a vertex. In this paper, we consider natural generalizations of these operations for binary matroids and explore their behaviour. We characterize all binary matroids obtainable from the binary projective geometry of rank $r$ under the operations of complementation and switching. Moreover, we show that not all binary matroids of rank at most $r$ can be obtained from a projective geometry of rank $r$ via a sequence of the three generalized operations. We introduce a fourth operation and show that, with this additional operation, we are able to obtain all binary matroids.

math.CO↗