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- W2015288268 abstract "Let χi(G) and Δ(G) denote the incidence coloring number and the maximum degree of a graph G, respectively. An easy observation shows that χi(G)⩾Δ(G)+1. In this paper, we consider incidence coloring number on hypercubes Qn. Based on the technique of Hamming codes, we present algorithms to obtain upper bounds of χi(Qn) for n in certain forms of integers. Let p,q be positive integers. We show that (1) χi(Qn)=n+1 if n=2p−1 for p⩾1; (2) χi(Qn)=n+2 if the following conditions hold: (i) n=2p−2 for p⩾2; (ii) n=2p+2q−2 for p,q⩾1; (iii) n=2p+2q−3 for p,q⩾2; and (3) χi(Qn)⩾n+2 otherwise." @default.
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- W2015288268 date "2014-11-01" @default.
- W2015288268 modified "2023-10-18" @default.
- W2015288268 title "Incidence coloring on hypercubes" @default.
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- W2015288268 doi "https://doi.org/10.1016/j.tcs.2014.08.017" @default.
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