In this paper, we study intersection assignments of graphs using multiple intervals for each vertex, where each interval is of identical length or in which no interval is properly contained in another. The resulting parameters unit interval number, i_u(G) and proper interval number, i_p(G) are shown to be equal for any graph G. Also, i_u(G) of a triangle-free graph G with maximum degree D is [(D + 1)/2] if G is regular and [D/2] otherwise.
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机译：在本文中，我们研究每个顶点使用多个间隔的图的相交分配，其中每个间隔的长度相同或其中另一个间隔中没有适当包含的间隔。结果得出的参数单位间隔数i_u（G）和适当间隔数i_p（G）对于任何图G都相等。而且，最大度D的无三角形图G的i_u（G）为[[ D + 1）/ 2]，如果G是常规的，否则为[D / 2]。
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