For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes＇in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimensi...For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes＇in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimension cube＇s, the minimum k required to represent G is called the cubicity of G. In this paper, a special graph .called unit-interval graph. IG[X, Y] is given, then 2n such graphs which have the same vertices as V（FQn） are constructed, where FQ, is the n-dimension folded hypercube. Thanks to the specia] structure of IG[X, Y], the result that cubicity（FQn）≤ 2n is proved.展开更多
文摘For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes＇in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimension cube＇s, the minimum k required to represent G is called the cubicity of G. In this paper, a special graph .called unit-interval graph. IG[X, Y] is given, then 2n such graphs which have the same vertices as V（FQn） are constructed, where FQ, is the n-dimension folded hypercube. Thanks to the specia] structure of IG[X, Y], the result that cubicity（FQn）≤ 2n is proved.
