A Stronger Bound for the Strong Chromatic Index
We prove χ′ s ( G ) ≤ 1.93 Δ( G ) 2 for graphs of sufficiently large maximum degree where χ′ s ( G ) is the strong chromatic index of G . This improves an old bound of Molloy and Reed. As a by-product, we present a Talagrand-type inequality where we are allowed to exclude unlikely bad outcomes that...
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| Veröffentlicht in: | Combinatorics, probability & computing probability & computing, 2018-01, Vol.27 (1), p.21-43 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove χ′
s
(
G
) ≤ 1.93 Δ(
G
)
2
for graphs of sufficiently large maximum degree where χ′
s
(
G
) is the strong chromatic index of
G
. This improves an old bound of Molloy and Reed. As a by-product, we present a Talagrand-type inequality where we are allowed to exclude unlikely bad outcomes that would otherwise render the inequality unusable. |
|---|---|
| ISSN: | 0963-5483 1469-2163 |
| DOI: | 10.1017/S0963548317000244 |