arXiv subjects

Hadi Alizadeh

Publications and source records attributed to Hadi Alizadeh.

4 recordsLinked to original sources

arXiv2026

Packing chromatic critical graphs with radius at most 2

For a graph $G$ with vertex set $V(G)$ and a positive integer $i$, an $i$-packing in $G$ is a subset $X$ of $V(G)$ such that the distance between any two distinct vertices of $X$ is greater than $i$. The packing chromatic number of $G$, denoted by $χ_ρ(G)$, is the smallest positive integer $k$ for which there exists a partition $X_1, X_2, \ldots, X_k$ of $V(G)$ such that $X_i$ is an $i$-packing in $G$ for every $i \in [k]$. A graph $G$ is called $χ_ρ$-critical if $χ_ρ(H) < χ_ρ(G)$ holds for every proper subgraph $H$ of $G$. In this paper, we provide a structural characterization of $χ_ρ$-critical graphs with radius $1$, and completely determine the $χ_ρ$-critical cactus graphs with radius $2$ and diameter $2$ or $3$.

math.CO↗

arXiv2024

Sharif-STR at SemEval-2024 Task 1: Transformer as a Regression Model for Fine-Grained Scoring of Textual Semantic Relations

Semantic Textual Relatedness holds significant relevance in Natural Language Processing, finding applications across various domains. Traditionally, approaches to STR have relied on knowledge-based and statistical methods. However, with the emergence of Large Language Models, there has been a paradigm shift, ushering in new methodologies. In this paper, we delve into the investigation of sentence-level STR within Track A (Supervised) by leveraging fine-tuning techniques on the RoBERTa transformer. Our study focuses on assessing the efficacy of this approach across different languages. Notably, our findings indicate promising advancements in STR performance, particularly in Latin languages. Specifically, our results demonstrate notable improvements in English, achieving a correlation of 0.82 and securing a commendable 19th rank. Similarly, in Spanish, we achieved a correlation of 0.67, securing the 15th position. However, our approach encounters challenges in languages like Arabic, where we observed a correlation of only 0.38, resulting in a 20th rank.

cs.CL↗

arXiv2021

Upper paired domination versus upper domination

A paired dominating set $P$ is a dominating set with the additional property that $P$ has a perfect matching. While the maximum cardainality of a minimal dominating set in a graph $G$ is called the upper domination number of $G$, denoted by $Γ(G)$, the maximum cardinality of a minimal paired dominating set in $G$ is called the upper paired domination number of $G$, denoted by $Γ_{pr}(G)$. By Henning and Pradhan (2019), we know that $Γ_{pr}(G)\leq 2Γ(G)$ for any graph $G$ without isolated vertices. We focus on the graphs satisfying the equality $Γ_{pr}(G)= 2Γ(G)$. We give characterizations for two special graph classes: bipartite and unicyclic graphs with $Γ_{pr}(G)= 2Γ(G)$ by using the results of Ulatowski (2015). Besides, we study the graphs with $Γ_{pr}(G)= 2Γ(G)$ and a restricted girth. In this context, we provide two characterizations: one for graphs with $Γ_{pr}(G)= 2Γ(G)$ and girth at least 6 and the other for $C_3$-free cactus graphs with $Γ_{pr}(G)= 2Γ(G)$. We also pose the characterization of the general case of $C_3$-free graphs with $Γ_{pr}(G)= 2Γ(G)$ as an open question.

math.CO↗

arXiv2018

Equimatchable Claw-Free Graphs

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm.

cs.DM↗