Work

Sparse Critical Graphs for Defective (1, 3)-Coloring

Year: 2025

Type: article

Abstract: A graph G is (1, 3)-colorable if its vertices can be partitioned into subsets $$V_1$$ V 1 and $$V_2$$ V 2 so that every vertex in $$G[V_1]$$ G [ V 1 ] has degree at most 1 and every vertex in $$G[V_2]$$ G [ V 2 ] has degree at most 3. We prove that every graph with maximum average degree at most 28/9 is (1, 3)-colorable.

Source: Graphs and Combinatorics

DOI: 10.1007/s00373-025-02973-y

Authors: Alexandr Kostochka, Jingwei Xu, Xuding Zhu

Institutions: University of Illinois Urbana-Champaign, Zhejiang Normal University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,190

Funders: National Science Foundation, National Natural Science Foundation of China, University of Illinois at Urbana-Champaign