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- W2549843525 abstract "An edge-coloured graph G is called properly connected if any two vertices are connected by a path whose edges are properly coloured. The proper connection number of a connected graph G , denoted by pc ( G ) , is the smallest number of colours that are needed in order to make G properly connected. Our main result is the following: Let G be a connected graph of order n and k ≥ 2 . If | E ( G ) | ≥ n − k − 1 2 + k + 2 , then pc ( G ) ≤ k except when k = 2 and G ∈ { G 1 , G 2 } , where G 1 = K 1 ∨ ( 2 K 1 + K 2 ) and G 2 = K 1 ∨ ( K 1 + 2 K 2 ) ." @default.
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- W2549843525 date "2017-11-01" @default.
- W2549843525 modified "2023-09-28" @default.
- W2549843525 title "Proper connection and size of graphs" @default.
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- W2549843525 doi "https://doi.org/10.1016/j.disc.2016.09.021" @default.
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