Unanswered Ask Question Is thinness of a graph NP-complete? up vote 19 down vote favorite 6 It is an easy fact that a graph is interval if and only if the vertices can be linear ordered in $v_1,\ldots,v_n$ so that for all $j$, the adjacents to $v_j$ in $\{v_1,\ldots,v_{j-1}\}$ are $\{v_{j-1},v_{j-2},\ldots,v_{j-t}\}$