منابع مشابه
Longest Path Problems on Ptolemaic Graphs
SUMMARY Longest path problem is a problem for finding a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, there are few known graph classes such that the longest path problem can be solved efficiently. Polynomial time algorithms for finding a longest cycle and a longest path in a Ptolemaic graph are pr...
متن کاملThe Longest Path Problem on Permutation Graphs
The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs.
متن کاملNew results on ptolemaic graphs
In this paper, we analyze ptolemaic graphs for its properties as chordal graphs. Firstly, two characterizations of ptolemaic graphs are proved. The first one is based on the reduced clique graph, a structure that was defined by Habib and Stacho [8]. In the second one, we simplify the characterization presented by Uehara and Uno [13] with a new proof. Then, known subclasses of ptolemaic graphs a...
متن کاملThe Longest Path Problem Is Polynomial on Interval Graphs
The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamiltonian path problem. Motivated by the work of Uehara and Uno in [22], where they left the longest path problem open for the class of interval graphs, ...
متن کاملProbe Ptolemaic Graphs
Given a class of graphs, G, a graph G is a probe graph of G if its vertices can be partitioned into two sets, P (the probes) and N (the nonprobes), where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. In this paper we study the probe graphs of ptolemaic graphs when the partition of vertices is unknown. We present some characteri...
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ژورنال
عنوان ژورنال: IEICE Transactions on Information and Systems
سال: 2008
ISSN: 0916-8532,1745-1361
DOI: 10.1093/ietisy/e91-d.2.170