arXiv subjects

Doel Rivera Laboy

Publications and source records attributed to Doel Rivera Laboy.

5 recordsLinked to original sources

arXiv2026

The scramble number of outerplanar graphs

For planar graphs, it is known that their treewidth is bounded by $O(\sqrt{n})$, where $n$ is the number of vertices of the graph. A related invariant to treewidth, is the scramble number of graphs. Recently, Connor et. al proved that planar graphs of bounded maximal degree have scramble number bounded by $O(\sqrt{n})$. An open question is whether the scramble number of any planar graph follows this same bound. We give a definitive answer with an explicit bound for a subset of planar graphs, the simple outerplanar graphs and the simple near outerplanar graphs.

math.CO↗

arXiv2026

On the gonality of Kneser graphs

The Kneser graphs $\text{KG}(n,k)$ are a classically studied family of graphs. One known invariant of graphs is gonality (also called divisorial gonality), which is the minimum degree of a rank 1 divisor on the graph. Using known bounds on gonality of simple, connected graphs, one may obtain that the gonality of $\text{KG}(n,k)$ is bounded above by $\binom{n-1}{k}$. In 2014, Harvey and Wood showed that the treewidth (a lower bound on gonality) for $\text{KG}(n,k)$ is $\binom{n-1}{k}-1$ for $n\geq 4k^2-3k+2$. In this paper, using scramble number, another lower bound on gonality, we improve this polynomial bound and show that the gonality of $\text{KG}(n,k)$ is exactly $\binom{n-1}{k}$ for $n\geq \frac{3k^2+k+2}{2}$, and conjecture an even stricter polynomial bound using the uniform edge scramble. We then extend our argument to the family of generalized Kneser Graphs, computing the scramble number and gonality using the same polynomial bound.

math.CO↗

arXiv2024

Fibonacci Sumsets and the Gonality of Strip Graphs

We provide a new perspective on the divisor theory of graphs, using additive combinatorics. As a test case for this perspective, we compute the gonality of certain families of outerplanar graphs, specifically the strip graphs. The Jacobians of such graphs are always cyclic of Fibonacci order. As a consequence, we obtain several results on the additive properties of Fibonacci numbers.

math.CO↗

arXiv2022

Affine Symplectic Grassmann codes

In this manuscript, we introduce a new class of linear codes, called affine symplectic Grassmann codes, and determine their parameters, automorphism group, minimum distance codewords, dual code and other key features. These linear codes are defined from an affine part of a polar symplectic Grassmannian. They combine polar symplectic Grassmann codes and affine Grassmann codes.

cs.IT↗

arXiv2021

Affine Hermitian Grassmann Codes

The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear code. We introduce a new class of linear codes, called Affine Hermitian Grassman Codes. These codes are the linear codes resulting from an affine part of the projection of the Polar Hermitian Grassmann codes. They combine Polar Hermitian Grassmann codes and Affine Grassmann codes. We will determine the parameters of these codes.

cs.IT↗