1-2hit |
Akira MATSUBAYASHI Shuichi UENO
The problem of constructing the proper-path-decomposition of width at most 2 has an application to the efficient graph layout into ladders. In this paper, we give a linear time algorithm which, for a given graph with maximum vertex degree at most 3, determines whether the proper-pathwidth of the graph is at most 2, and if so, constructs a proper-path-decomposition of width at most 2.
Atsushi TAKAHASHI Shuichi UENO Yoji KAJITANI
We introduce the interval set of a graph G which is a representation of the proper-path-decomposition of G, and show a linear time algorithm to construct an optimal interval set for any tree T. It is shown that a proper-path-decomposition of T with optimal width can be obtained from an optimal interval set of T in O(n log n) time.