Academic Journal
Asymptotically Optimal Proper Conflict‐Free Coloring: Asymptotically optimal proper conflict-free coloring
| Title: | Asymptotically Optimal Proper Conflict‐Free Coloring: Asymptotically optimal proper conflict-free coloring |
|---|---|
| Authors: | Chun‐Hung Liu, Bruce Reed |
| Source: | Random Structures & Algorithms. 66 |
| Publication Status: | Preprint |
| Publisher Information: | Wiley, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Connectivity, Extremal problems in graph theory, graph colouring, Coloring of graphs and hypergraphs, Lovász local lemma, FOS: Mathematics, Mathematics - Combinatorics, Vertex degrees, 0102 computer and information sciences, Combinatorics (math.CO), 0101 mathematics, quasi-random method, 01 natural sciences |
| Description: | 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. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1098-2418 1042-9832 |
| DOI: | 10.1002/rsa.21285 |
| DOI: | 10.48550/arxiv.2401.02155 |
| Access URL: | http://arxiv.org/abs/2401.02155 https://zbmath.org/8036330 https://doi.org/10.1002/rsa.21285 |
| Rights: | Wiley Online Library User Agreement arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....d2e50859fae5d4b00b6703a1a93fa77f |
| Database: | OpenAIRE |
| ISSN: | 10982418 10429832 |
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| DOI: | 10.1002/rsa.21285 |