Linear structure of bipartite permutation graphs and the longest path problem
نویسندگان
چکیده
منابع مشابه
Linear structure of bipartite permutation graphs and the longest path problem
The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application o...
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 کاملOptimal Path Cover Problem on Block Graphs and Bipartite Permutation Graphs
The optimal path cover problem is to find a minimum number of vertex disjoint paths which together cover all the vertices of the graph. Finding an optimal path cover for an arbitrary graph is known to be NP-complete [3]. However, polynornial-time algorithms exist for trees [4], cacti [4] and for interval graphs [9]. The solution presented in [2] For circular-arc graphs is known to be wrong. In ...
متن کاملComputing the Cutwidth of Bipartite Permutation Graphs in Linear Time
The problem of determining the cutwidth of a graph is a notoriously hard problem which remains NP-complete under severe restrictions on input graphs. Until recently, nontrivial polynomial-time cutwidth algorithms were known only for subclasses of graphs of bounded treewidth. Very recently, Heggernes et al. (SIAM J. Discrete Math., 25 (2011), pp. 1418–1437) initiated the study of cutwidth on gra...
متن کاملOn the linear structure and clique-width of bipartite permutation graphs
Bipartite permutation graphs have several nice characterizations in terms of vertex ordering. Besides, as AT-free graphs, they have a linear structure in the sense that any connected bipartite permutation graph has a dominating path. In the present paper, we elaborate the linear structure of bipartite permutation graphs by showing that any connected graph in the class can be stretched into a "p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2007
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2007.02.010