Geodesic
Induced $nK_{2}$ decomposition of infinite square grids and infinite hexagonal grids
Ural mathematical journal, Tome 8 (2022) no. 1, pp. 23-33

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The induced $nK_2$ decomposition of infinite square grids and hexagonal grids are described here. We use the multi-level distance edge labeling as an effective technique in the decomposition of square grids. If the edges are adjacent, then their color difference is at least $2$ and if they are separated by exactly a single edge, then their colors must be distinct. Only non-negative integers are used for labeling. The proposed partitioning technique per the edge labels to get the induced $nK_2$ decomposition of the ladder graph is the square grid and the hexagonal grid.
Keywords: distance labelling, channel assignment, $L(h,k)$-colouring, rectangular grid
Mots-clés : hexagonal grid. 
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     author = {Dinesan Deepthy and Joseph Varghese Kureethara},
     title = {Induced $nK_{2}$ decomposition of infinite square grids and infinite hexagonal grids},
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     publisher = {mathdoc},
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     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a2/}
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Dinesan Deepthy; Joseph Varghese Kureethara. Induced $nK_{2}$ decomposition of infinite square grids and infinite hexagonal grids. Ural mathematical journal, Tome 8 (2022) no. 1, pp. 23-33. http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a2/