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—We propose a new 3D barcode standard, Quick Layered Response (QLR) codes, and implemented encoding and decoding on Android devices. QLR codes are Quick Response (QR) codes superimposed in the RGB color space, and increase the capacity by a factor of 3. This advantage can be used to decrease the area needed to represent data by a factor of 3 or to increase(More)
We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ (k) (G). We prove bounds on χ (k) (G) for all graphs G, including corollaries for outerplanar and planar graphs. We also define the k-clique-relaxed game chromatic number, χ (k) g (G), of a graph G. We prove χ (2) g (G) ≤ 4 for all(More)
The (r, d)-relaxed coloring game is a two-player game played on the vertex set of a graph G. We consider a natural analogue to this game on the edge set of G called the (r, d)-relaxed edge-coloring game. We consider this game on trees and more generally, on k-degenerate graphs. We show that if G is k-degenerate with ∆(G) = ∆, then the first player, Alice,(More)
We investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color {\alpha} is legal for a vertex if said vertex has no neighbors colored {\alpha}. Other variations of the game change this(More)
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