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Topic: Cograph

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	Papers Report (Site not responding. Last check: 2007-11-05)
		A graph is called complement reducible (a cograph for short) if every its induced subgraph with at least two vertices is either disconnected or the complement to a disconnected graph.
		The bipartite analog of cographs, bi-complement reducible graphs, has been characterized recently by three forbidden induced subgraphs: $Star_{1,2,3}$, $Sun_4$ and $P_7$, where $Star_{1,2,3}$ is the graph with vertices $a,b,c,d,e,f,g$ and edges $(a,b)$, $(b,c)$, $(c,d)$, $(d,e)$, $(e,f)$, $(d,g)$, and $Sun_4$ is the graph with vertices $a,b,c,d,e,f,g,h$ and edges $(a,b)$, $(b,c)$, $(c,d)$, $(d,a)$, $(a,e)$, $(b,f)$, $(c,g)$, $(d,h)$.
		Based on the proposed characterization we prove that the clique-width of these graphs is at most five that leads to polynomial algorithms for a number of problems which are NP-complete in general bipartite graphs.
	www.mfcs.sk /mfcs2000/abstracts/AccAbs3.html (143 words)

	Search results (Site not responding. Last check: 2007-11-05)
		A graph $G$ is defined to be a cograph contraction if it is obtained from a cograph $H$ by contracting some pairwise disjoint independent sets and then making the contracted vertices pairwise adjacent.
		These conditions imply that cograph contractions are weakly triangulated graphs, that means, graphs without induced $C_\ell$ and $\overline C_\ell$ $(\ell\ge 5)$.\par In Section 3 the main result of this paper is given by Theorem 3.1: A graph $G$ is a cograph contraction iff it has a clique satisfying the $P_4$-condition and the $\overline P_5$-condition.
		Therefore, the author also investigates the case of a connected cograph $H$.\par Section 6 contains the following result: A graph $G$ is a connected-cograph contraction iff it is the join of two cograph contractions (Theorem 6.1).
	wwwdb.informatik.uni-rostock.de /~le/Public/VBL4.html (235 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		We show that the notoriously difficult problem of finding and reporting the smallest number of vertex-disjoint paths that cover the vertices of a graph can be solved time- and work-optimally for cographs.
		Our result implies that for this class of graphs the task of finding a Hamiltonian path can be solved time- and work-optimally in parallel.It was open for more than 10 years to find a time- and work-optimal parallel solution for this important problem.
		We then go on to show that this time lower bound is tight by devising an EREW algorithm that, given an n-vertex cograph G represented by its cotree, finds and reports all the paths in a minimum path cover in O(logn) time using n/logn processors.
	www.elsevier.com /cdweb/journals/03043975/articles/290/3/S030439750200068.abstract.en (165 words)

	[No title]
		We know linear time colouring algorithm for cographs, given their cotree (which can be constructed efficiently from graph).
		Fact: G is a cograph iff G does NOT contain any induced copy of P4, i.e., G does not contain 4 vertices s,t,u,v with only edges (s,t), (t,u), and (u,v) (either one of these edges missing, or some other edge present between s,t,u,v).
		Detecting if G is cograph takes time Omega(n^4) (potentially must examine all groups of 4 vertices), so not a good idea.
	www.cs.toronto.edu /~fpitt/CSC366/20031/heuristics.txt (650 words)

	Monadic Second-Order Logic-11; abstract (Site not responding. Last check: 2007-11-05)
		It is also possible to use monadic second-order logic to express graph transformations and functions on graphs.
		The unique decomposition of a cograph is definable in this way (in a precise sense) by MS formulas, provided the graph is given with an auxiliary linear ordering.
		In the present paper, we investigate in this perspective the unique decomposition of connected graphs defined by Tutte and we prove that it is definable by MS-formulas.
	www.labri.u-bordeaux.fr /Perso/~courcell/Art11.html (343 words)

	Expert About co:Commutative
		In the commutative case the formula is viewed as a cograph.
		In the non-commutative case it is a more complicated kind of graph which is, roughly speaking, a directed cograph.
		The criterion consists in the commutative condition plus a bracketing condition.
	www.expertsite.biz /dir/co/commutative.htm (1314 words)

	cograph graphs (Site not responding. Last check: 2007-11-05)
		G is a cograph (short for complement-reducible graph) if one of the following equivalent conditions hold:
		G can be constructed from isolated vertices by disjoint union and join operations.
		split cograph contraction distance-hereditary parity strong tree-cograph tree-cograph
	wwwteo.informatik.uni-rostock.de /isgci/classes/gc_151.html (246 words)

	Selected publications at LSV:
		Local temporal logic is expressively complete for cograph dependence alphabets.
		The main result of the paper shows such an expressive completeness result, if the underlying dependence alphabet is a cograph, i.e.
		Moreover, we show that this is the best we can expect in our setting: If the dependence alphabet is not a cograph, then we cannot express all first order properties.
	www.lsv.ens-cachan.fr /Publis/publis.php?filename=lsv&onlykey=icomp-DG2004 (150 words)

	A Fully Dynamic Algorithm for Modular Decomposition and Recognition of Cographs (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		A Fully Dynamic Algorithm for Modular Decomposition and Recognition of Cographs
		Abstract: The problem of dynamically recognizing a graph property calls for efficiently deciding if an input graph satisfies the property under repeated modifications to its set of vertices and edges.
		85 A linear recognition algorithm for cographs (context) - Corneil, Perl et al.
	sherry.ifi.unizh.ch /563519.html (415 words)

	[No title]
		These relationships may be represented as a digraph, where the nodes model the data items, and the edges model the relationships.
		It is shown that recognition, transitive orientation, maximum node weighted clique, minimum node coloring, minimum weight dominating set, minimum fill-in and isomorphism for cographs is in NC.
		A remarkable property of $P_4$-reducible graphs is their unique tree representation up to isomorphism.
	www.ics.uci.edu /~eppstein/bibs/subiso.bib (13928 words)

	DBLP: Paul Gastin
		Paul Gastin, Pierre Moro, Marc Zeitoun: Minimization of Counterexamples in SPIN.
		Volker Diekert, Paul Gastin: Local temporal logic is expressively complete for cograph dependence alphabets.
		Paul Gastin, Dietrich Kuske: Satisfiability and Model Checking for MSO-definable Temporal Logics are in PSPACE.
	www.vldb.org /dblp/db/indices/a-tree/g/Gastin:Paul.html (617 words)

	Draw Selected Graph Classes (Site not responding. Last check: 2007-11-05)
		Moreover, you can select all classes and remove classes from the right list box.
		In this example we have selected ten graph classes (HHD--free, chordal, cograph,...).
		By pressing on the Draw button the inclusion hierarchy of the selected graph classes will be shown:
	www.informatik.uni-rostock.de /~gdb/isgci12/doc/Applet/drawselected.html (101 words)

	2003-36: A solution to a problem of Le (Site not responding. Last check: 2007-11-05)
		A graph $G$ is called a {\em cograph contraction} if there exist a cograph $H$ and pairwise disjoint non-empty stable sets in $H$ for which $G \simeq H^*$.
		Solving a problem proposed by Le~\cite{Le99}, we give a finite forbidden induced subgraph characterization of cograph contractions.
		{\bf Keywords:} {Cograph contractions, perfect graphs,weakly chordal graphs, forbidden induced subgraphs}.
	dimacs.rutgers.edu /TechnicalReports/abstracts/2003/2003-36.html (140 words)

	Graph Searching and Interval Completion
		Then, making use of monotone properties, we prove that for any graph G the search cost of G is equal to the smallest number of edges of all interval supergraphs of G.
		Finally, we show how to compute the search cost of a cograph and the corresponding search strategy in linear time.
		graph searching, search cost, vertex separation, interval graph completion, linear layout, profile, cograph
	epubs.siam.org /sam-bin/dbq/article/35047 (176 words)

	DBLP: Christophe Paul (Site not responding. Last check: 2007-11-05)
		Michel Habib, Fabien de Montgolfier, Christophe Paul: A Simple Linear-Time Modular Decomposition Algorithm for Graphs, Using Order Extension.
		Christophe Crespelle, Christophe Paul: Fully-Dynamic Recognition Algorithm and Certificate for Directed Cographs.
		Cyril Gavoille, Christophe Paul: Optimal Distance Labeling for Interval and Circular-Arc Graphs.
	dblp.uni-trier.de /db/indices/a-tree/p/Paul:Christophe.html (343 words)

	DBLP: Michel Habib (Site not responding. Last check: 2007-11-05)
		Michel Habib, Christophe Paul: A simple linear time algorithm for cograph recognition.
		Michel Habib, Emmanuelle Lebhar, Christophe Paul: A note on finding all homogeneous set sandwiches.
		Guillaume Damiand, Michel Habib, Christophe Paul: A simple paradigm for graph recognition: application to cographs and distance hereditary graphs.
	www.informatik.uni-trier.de /~ley/db/indices/a-tree/h/Habib:Michel.html (609 words)

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