Work

Asymptotically Optimal Proper Conflict‐Free Coloring

Year: 2025

Type: article

Abstract: ABSTRACT A proper conflict‐free coloring of a graph is a coloring of the vertices such that any two adjacent vertices receive different colors, and for every non‐isolated vertex , some color appears exactly once on the neighborhood of . Caro, Petruševski and Škrekovski conjectured that every connected graph with maximum degree has a proper conflict‐free coloring with at most colors. This conjecture holds for and remains open for . In this article we prove that this conjecture holds asymptotically; namely, every graph with maximum degree has a proper conflict‐free coloring with colors.

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.21285

Authors: Chun‐Hung Liu, Bruce Reed

Institutions: Texas A&M University, Institute of Mathematics, Academia Sinica

Language: English

Topic: Graph Labeling and Dimension Problems

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science and Technology Council, National Science Foundation, Academia Sinica, National Science and Technology Council

Awards: The Combinatorics of Complex Networks, CAREER: Graph Structural Theorems, Asymptotic Dimension, and Beyond, Graph Decompositions and Their Applications, G6671297155