Induced Nk2 Decomposition of Infinite Square Grids and Infinite Hexagonal Grids

Abstract

The induced nK2 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 nK2 decomposition of the ladder graph is the square grid and the hexagonal grid.