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In this paper, we present a linear-time algorithm for substitution decomposition on chordal graphs. Based on this result, we develop a linear-time algorithm for transitive orientation on chordal comparability graphs, which reduces the complexity of chordal comparability recognition from O(n) to O(n+m). We also devise a simple linear-time algorithm for(More)
The k-chain subgraph cover problem asks if the edge set of a given bipartite graph G is the union of the edge sets of k chain graphs, where each chain graph is a subgraph of G. Although the X--chain subgraph cover problem is known to be NP-complete for the class of bipartite graphs, it is still unknown whether this problem is NP-complete or polynomial-time(More)
The split decomposition of a graph, which is also known as the join decomposition [GHS], ms], was developed by Cunningham [Cu] . Originally, the decomposition was seen primarily as a tool for dealing with directed graphs. Recently, however, the undirected version of this decomposition has been used as part of efficient algorithms for dealing with a number(More)