Detecting 2-joins faster

2-joins are edge cutsets that naturally appear in the decomposition of several classes of graphs closed under taking induced subgraphs, such as balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free graphs. Their detection is needed in several algorithms, and is the slowest step for some of them. The classical method to detect a 2-join takes O(nm) time where n is the number of vertices of the input graph and m the number of its edges. To detect non-path 2-joins (special kinds of 2-joins that are needed in all of the known algorithms that use 2-joins), the fastest known method takes time O(nm). Here, we give an O(nm)-time algorithm for both of these problems. A consequence is a speed up of several known algorithms. Université Paris 7, LIAFA, Case 7014, 75205 Paris Cedex 13, France. E-mail: pierre.charbit. Université Paris 7, LIAFA, Project team Inria : Gang, Case 7014, 75205 Paris Cedex 13, France. E-mail: [email protected]. CNRS, LIP ENS de Lyon, INRIA, Université de Lyon, 15 parvis René Descartes BP 7000 69342 Lyon cedex 07 France. Email: [email protected]. School of Computing, University of Leeds, Leeds LS2 9JT, UK and Faculty of Computer Science, Union University, Knez Mihailova 6/VI, 11000 Belgrade, Serbia. E-mail: [email protected]. Partially supported by EPSRC grant EP/H021426/1 and Serbian Ministry of Education and Science grants 174033 and III44006. The first and third authors are supported by Agence Nationale de la Recherche under reference anr 10 jcjc 0204 01. The four authors are also supported by PHC Pavle Savić grant, jointly awarded by EGIDE, an agency of the French Ministère des Affaires étrangères et européennes, and Serbian Ministry for Science and Technological Development.