TL;DR
This paper presents a general lemma for partitioning graph vertices into subgraphs with bounded degree, extending previous foundational results in graph theory.
Contribution
It introduces a new, broad lemma that generalizes earlier work by Lovász, Catlin, Kostochka, and Rabern on vertex partitions.
Findings
Provides a unifying lemma for vertex partitioning
Extends classical results in graph theory
Offers potential applications in graph coloring and structure analysis
Abstract
We prove a general lemma about partitioning the vertex set of a graph into subgraphs of bounded degree. This lemma extends a sequence of results of Lov\'asz, Catlin, Kostochka and Rabern.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Advanced Combinatorial Mathematics