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• W2592362234 abstract "The least $k$ admitting a proper edge colouring $c:Eto{1,2,ldots,k}$ of a graph $G=(V,E)$ without isolated edges such that $sum_{eni u}c(e)neq sum_{eni v}c(e)$ for every $uvin E$ is denoted by $chi'_{Sigma}(G)$. It has been conjectured that $chi'_{Sigma}(G)leq Delta + 2$ for every connected graph of order at least three different from the cycle $C_5$, where $Delta$ is the maximum degree of $G$. It is known that $chi'_{Sigma}(G) = Delta + O(Delta^frac{5}{6}ln^frac{1}{6}Delta)$ for a graph $G$ without isolated edges. We improve this upper bound to $chi'_{Sigma}(G) = Delta + O(Delta^frac{1}{2})$ using a simpler approach involving a combinatorial algorithm enhanced by the probabilistic method. The same upper bound is provided for the total version of this problem as well." @default.
• W2592362234 created "2017-03-16" @default.
• W2592362234 creator A5009715410 @default.
• W2592362234 date "2019-03-01" @default.
• W2592362234 modified "2023-10-03" @default.
• W2592362234 title "A note on asymptotically optimal neighbour sum distinguishing colourings" @default.
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• W2592362234 doi "https://doi.org/10.1016/j.ejc.2018.10.009" @default.
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