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- W3039485391 abstract "Abstract An edge-coloured graph $G$ is called properly connected if any two vertices are connected by a properly coloured path. The proper connection number, $pc(G)$ , of a graph $G$ , is the smallest number of colours that are needed to colour $G$ such that it is properly connected. Let $unicode[STIX]{x1D6FF}(n)$ denote the minimum value such that $pc(G)=2$ for any 2-connected incomplete graph $G$ of order $n$ with minimum degree at least $unicode[STIX]{x1D6FF}(n)$ . Brause et al. [‘Minimum degree conditions for the proper connection number of graphs’, Graphs Combin. 33 (2017), 833–843] showed that $unicode[STIX]{x1D6FF}(n)>n/42$ . In this note, we show that $unicode[STIX]{x1D6FF}(n)>n/36$ ." @default.
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- W3039485391 date "2020-07-03" @default.
- W3039485391 modified "2023-09-27" @default.
- W3039485391 title "NOTE ON MINIMUM DEGREE AND PROPER CONNECTION NUMBER" @default.
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- W3039485391 doi "https://doi.org/10.1017/s0004972720000593" @default.
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