Improved book-embeddings of incomplete hypercubes

Abstract

a b s t r a c tIn this paper, we show that any incomplete hypercube with, at most, 2 n + 2 n−1 + 2 n−2 vertices can be embedded in n − 1 pages for all n ≥ 4. For the case n ≥ 4, this result improves Fang and Lai's result that any incomplete hypercube with, at most, 2 n + 2 n−1 vertices can be embedded in n − 1 pages for all n ≥ 2.Besides this, we show that the result can be further improved when n is largee.g., any incomplete hypercube with at most 2 n + 2 n−1 + 2 n−2 + 2 n−7 (respectively, 2 n + 2 n−1 + 2 n−2 + 2 n−7 + 2 n−230 ) vertices can be embedded in n − 1 pages for all n ≥ 9 (respectively, n ≥ 232).