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Given a sequence S = (s₁, s₂, , sₖ) of positive integers with s₁ s₂ sₖ, an S-packing coloring of a graph G is a partition of V (G) into k subsets V₁, V₂, , Vₖ such that for each 1 i k the distance between any two distinct x, y Vᵢ is at least sᵢ + 1. In 2023, Yang and Wu proved that all 3-irregular subcubic graphs are (1, 1, 3) -packing colorable. In 2024, Mortada and Togni proved that every 1-saturated subcubic graph is (1, 1, 2) -packing colorable. In this paper, we provide new, concise proofs for these two theorems using a novel tool.
Hadeel Al Bazzal (Tue,) studied this question.