On Cotree-Critical and DFS Cotree-Critical Graphs
نویسندگان
چکیده
We give a characterization of DFS cotree-critical graphs which is central to the linear time Kuratowski finding algorithm implemented in PIGALE (Public Implementation of a Graph Algorithm Library and Editor [2]) by the authors, and deduce a justification of a very simple algorithm for finding a Kuratowski subdivision in a DFS cotree-critical graph. Communicated by: P. Mutzel and M. Jünger; submitted May 2002; revised August 2003. de Fraysseix & Ossona de Mendez, Critical Graphs, JGAA, 7(4) 411–427 (2003) 412
منابع مشابه
Trémaux Trees and Planarity
We present two characterizations of planarity based on Trémaux trees (i.e. DFS trees). From the last one, we deduce a simple and efficient planarity test algorithm which is eventually a new implementation of the Hopcroft Tarjan planarity algorithm. We finally recall a theorem on “cotree critical non-planar graphs” which very much simplify the search of a Kuratowski subdivision in a non-planar g...
متن کاملA Novel Algebraic Multigrid-Based Approach for Maxwell’s Equations
This paper presents a new algebraic multigrid-based method for solving the curl-curl formulation of Maxwell’s equations discretized with edge elements. The ultimate goal of this approach is two-fold. The first is to produce a multiple-coarsening multigrid method with two approximately decoupled hierarchies branching off at the initial coarse level, one resolving the divergence-free error and th...
متن کاملCograph Recognition Algorithm Revisited and Online Induced P4 Search
In 1985, Corneil, Perl and Stewart CPS85] gave a linear incremental algorithm to recognize cographs (graphs with no induced P4). When this algorithm stops, either the initial graph is a cograph and the cotree of the whole graph has been built, or the initial graph is not a cograph and this algorithm ends up with a vertex v and a cotree cot such that v cannot be inserted in cot; so the input gra...
متن کاملOn Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions
Symbolic ultrametrics define edge-colored complete graphs Kn and yield a simple tree representation of Kn. We discuss, under which conditions this idea can be generalized to find a symbolic ultrametric that, in addition, distinguishes between edges and non-edges of arbitrary graphs G = (V,E) and thus, yielding a simple tree representation of G. We prove that such a symbolic ultrametric can only...
متن کاملManaging Large Scale Computational Markets
General equilibrium theory has been proposed for resource allocation in computational markets. The basic procedure is that agents submit bids and that a resource (re)allocation is performed when a set of prices (one for each commodity) is found such that supply meets demand for each commodity. For successful implementation of large markets based on general equilibrium theory, ee-cient algorithm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Graph Algorithms Appl.
دوره 7 شماره
صفحات -
تاریخ انتشار 2003