Improved book-embeddings of incomplete hypercubes

Toru Hasunuma
2009 Discrete Applied Mathematics  
In 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
more » ... 2 + 2 n−7 + 2 n−230 ) vertices can be embedded in n − 1 pages for all n ≥ 9 (respectively, n ≥ 232).
doi:10.1016/j.dam.2008.10.008 fatcat:oq64mtmeargsnewktqljcqd3my