Academic Journal
Asymptotically Optimal Proper Conflict‐Free Coloring: Asymptotically optimal proper conflict-free coloring
| Τίτλος: | Asymptotically Optimal Proper Conflict‐Free Coloring: Asymptotically optimal proper conflict-free coloring |
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| Συγγραφείς: | Chun‐Hung Liu, Bruce Reed |
| Πηγή: | Random Structures & Algorithms. 66 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Wiley, 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | 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 |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1098-2418 1042-9832 |
| DOI: | 10.1002/rsa.21285 |
| DOI: | 10.48550/arxiv.2401.02155 |
| Σύνδεσμος πρόσβασης: | 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 |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....d2e50859fae5d4b00b6703a1a93fa77f |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 10982418 10429832 |
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| DOI: | 10.1002/rsa.21285 |