A. Pastine

activity

20122026

most citedOn the Hamilton-Waterloo Problem with triangle factors and

C_{3 x}

-factors

14 citations · 24 across the 27 of their papers we have counts for

collaborators

30 papers

math.CO2026

On the spectrum and expansion of graph associahedra

Ana Gargantini, Adrián Pastine, Pablo Torres +1

In this article, we contribute to the spectral analysis of graph associahedra by providing a lower bound for the second largest eigenvalue of $A (G)$ . Furthermore, using e…

math.GR2026

On $R$ -sequenceability of odd ordered groups

Adrián Pastine, María Valentina Soldera Ruiz

We study the $R$ -sequenceability of finite groups of odd order. Building on the classical theory of $R^{*}$ -sequences and orthomorphisms, we explore two tools: the notion of $R^{**}$ …

math.CO2026

Commutative Distance-Regularity: Algebraic Hierarchies and Cayley Graph Constructions

Agustín Oromí, Adrián Pastine

This paper resolves several open questions regarding the algebraic and metric inheritance of distance-based regularities under graph products, with a particular focus on Commutativ…

math.CO2026

Induced paths and cycles in factor graphs of split graphs

Victor N. Schvöllner, Adrián Pastine

Let $S$ be a split graph with bipartition $(K, I)$ and let $Φ (S)$ be the factor graph associated with $S$ , a multigraph on $I$ whose encodes the combinatorial information about 2-sw…

math.CO2026

Inequalities Involving Core, Corona, and Critical Sets in General Graphs

Adrián Pastine, Kevin Pereyra

Let $α (G)$ denote the cardinality of a maximum independent set. An independent set $I$ of $G$ is critical if $∣ I ∣ - ∣ N (I) ∣ \geq ∣ J ∣ - ∣ N (J) ∣$ f…

math.CO2026

2-switch: transition and stability on forests and pseudofests

Victor N. Schvöllner, Adrián Pastine, Daniel A. Jaume

Given any two forests (pseudoforests) with the same degree sequence, we show that one can be transformed into the other by a sequence of 2-switches in such a way that all the inter…

math.CO2025

Simple factor graphs associated with split graphs

Victor Nicolas Schvöllner, Adrian Pastine

We introduce and study a loopless multigraph associated with a split graph $(S, K, I)$ : its factor graph $Φ (S, K, I)$ , whose vertex set is $I$ and whose edges, counted with multiplicit…

math.CO2025

The 2-switch-degree of a graph

Victor N. Schvöllner, Adrián Pastine

In this work, we study the 2-switch-degree of a graph $G$ , that is, the degree of $G$ as a vertex of the realization graph $G (d)$ associated with the degree sequence $d$ …

math.CO2025

Totally odd subdivisions in Kneser graphs

Henry Echeverría, Andrea Jiménez, Suchismita Mishra +3

As evidence for the Odd Hadwiger Conjecture, Simonyi and Zsbán (2010) showed that every Kneser graph $G$ with large enough order (compared to $χ (G)$ ) contains a totally odd subdivi…

math.CO2024

Effect of graph operations on graph associahedra

Ana Gargantini, Adrián Pastine, Pablo Torres

Given a graph $G$ , we determine the structure of the rotation graph of a graph obtained by applying certain operations to $G$ . Specifically, we consider the operations of adding a…

math.CO2024

Exact distance Kneser graphs

Agustina Victoria Ledezma, Adrián Pastine, Mario Valencia-Pabon

For any graph $G = (V, E)$ and positive integer $d$ , the exact distance- $d$ graph $G_{= d}$ is the graph with vertex set $V$ , where two vertices are adjacent if and only if the dista…

math.CO2024★ 1 cited

$s$ -Stable Kneser Graph are Hamiltonian

Agustina V. Ledezma, Adrián G. Pastine

The Kneser Graph $K (n, k)$ has as vertices all $k$ -subsets of ${1, \dots, n}$ and edges connecting two vertices if they are disjoint. The $s$ -stable Kneser Graph $K_{s - s t ab} (n, k)$ …

math.CO2023★ 4 cited

Biclique immersions in graphs with independence number 2

Fábio Botler, Andrea Jiménez, Carla N. Lintzmayer +3

The analogue of Hadwiger's conjecture for the immersion relation states that every graph $G$ contains an immersion of $K_{χ (G)}$ . For graphs with independence number 2, this is equ…

math.CO2022

Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem

A. C. Burgess, P. Danziger, A. Pastine +1

In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group $G$ . When $G$ is cyclic, these types of matrices have been widely used to build uniform…

math.CO2022

On the rank of the distance matrix of graphs

Ezequiel Dratman, Luciano N. Grippo, Verónica Moyano +1

Let $G$ be a connected graph with $V (G) = {v_{1}, \dots, v_{n}}$ . The $(i, j)$ -entry of the distance matrix $D (G)$ of $G$ is the distance between $v_{i}$ and $v_{j}$ . In this article, using…

math.CO2021

On the diameter of Schrijver graphs

Agustina Victoria Ledezma, Adrián Pastine, Pablo Torres +1

For $k \geq 1$ and $n \geq 2 k$ , the well known Kneser graph $KG (n, k)$ has all $k$ -element subsets of an $n$ -element set as vertices; two such subsets are adjacent if…

math.CO2021

2-switch transition on unicyclic graphs and pseudoforest

Daniel A. Jaume, Adrián Pastine, Victor Schvöllner

In the present work we prove that given any two unicycle graphs (pseudoforests) that share the same degree sequence there is a finite sequence of 2-switches transforming one into t…

math.CO2020

On Stars in Caterpillars and Lobsters

Emiliano J. J. Estrugo, Adrián Pastine

The family of all $k$ -independent sets of a graph containing a fixed vertex $v$ is called a {star} and $v$ is called its center. Stars are interesting for their relation to Erdös-K…

math.CO2020★ 2 cited

2-switch: transition and stability on graphs and forests

Daniel A. Jaume, Adrián Pastine, Victor Nicolas Schvöllner

Given any two forests with the same degree sequence, we show in an algorithmic way that one can be transformed into the other by a sequence of 2-switches in such a way that all the…

math.CO2019

Sequencing Partial Steiner Triple Systems

Brian Alspach, Donald L. Kreher, Adrián Pastine

A partial Steiner triple system of order n is sequenceable if there is a sequence of length n of its distinct points such that no proper segment of the sequence is a union of point…

math.CO2018

Short note on Randić energy

Luiz Emilio Allem, Gonzalo Molina, Adrián Pastine

In this paper, we consider the Randić energy $R E$ of simple connected graphs. We provide upper bounds for $R E$ in terms of the number of vertices and the nullity of the graph. We p…

math.CO2018

On the null structure of bipartite graphs without cycles of length a multiple of 4

Daniel A. Jaume, Gonzalo Molina, Adrián Pastine

In this work we study the null space of bipartite graphs without cycles of length multiple of $4$ , and its relation to structural properties. We decompose them into two subgraphs:…

math.CO2018

The number of s-separated k-sets in various circles

Emiliano J. J. Estrugo, Adrián Pastine

This article studies the number of ways of selecting $k$ objects arranged in $p$ circles of sizes $n_{1}, \dots, n_{p}$ such that no two selected ones have less than $s$ objects between…

math.CO2018★ 1 cited

On the structure of the fundamental subspaces of acyclic matrices with $0$ in the diagonal

Daniel A. Jaume, Adrián Pastine

A matrix is called acyclic if replacing the diagonal entries with $0$ , and the nonzero diagonal entries with $1$ , yields the adjacency matrix of a forest. In this paper we show tha…

On the spectrum and expansion of graph associahedra

On R-sequenceability of odd ordered groups

Commutative Distance-Regularity: Algebraic Hierarchies and Cayley Graph Constructions

Induced paths and cycles in factor graphs of split graphs

Inequalities Involving Core, Corona, and Critical Sets in General Graphs

2-switch: transition and stability on forests and pseudofests

Simple factor graphs associated with split graphs

The 2-switch-degree of a graph

Totally odd subdivisions in Kneser graphs

Effect of graph operations on graph associahedra

Exact distance Kneser graphs

s-Stable Kneser Graph are Hamiltonian

Biclique immersions in graphs with independence number 2

Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem

On the rank of the distance matrix of graphs

On the diameter of Schrijver graphs

2-switch transition on unicyclic graphs and pseudoforest

On Stars in Caterpillars and Lobsters

2-switch: transition and stability on graphs and forests

Sequencing Partial Steiner Triple Systems

Short note on Randić energy

On the null structure of bipartite graphs without cycles of length a multiple of 4

The number of s-separated k-sets in various circles

On the structure of the fundamental subspaces of acyclic matrices with 0 in the diagonal

On $R$ -sequenceability of odd ordered groups

$s$ -Stable Kneser Graph are Hamiltonian

On the structure of the fundamental subspaces of acyclic matrices with $0$ in the diagonal