Open - Interval Graphs versus Closed - Interval Grap
نویسنده
چکیده
A graph G = (V, E) is said to be represented by a family F of nonempty sets if there is a bijection f:V--*F such that uv ~ E if and only iff(u)Nf(v)q=~. It is proved that if G is a countable graph then G can be represented by open intervals on the real line if and only if G can be represented by closed intervals on the real line, however, this is no longer true when G is an uncountable graph. Similar results are also proved when intervals are required to have unit length.
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