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Topic: Subgraphs

Related Topics

Subgraph isomorphism problem

Topological sorting

Graph theory

List of graph theory topics

Complete graph

Directed acyclic graph

Graph homomorphism

Planar graph

Graph rewriting

Perfect graph

Cycle space

Instruction scheduling

Max flow min cut theorem

Flood fill

MUD trees

	Identifying Subgraphs of Dependency
		The addition of variables onto the subgraph so that at least one additional variable in the seed is now covered (has no constraints outside the new subgraph).
		The combination of two subgraphs so that at least one new variable that wasn't covered in either of the two subgraphs alone is now covered.
		The input complexity of subgraph 2 is the output complexity of subgraph 1 (1), plus the number of variables added (4), for a total of 5.
	crl.nmsu.edu /users/sb/papers/thesis/node38.html (1073 words)

	Computation of Subgraphs (Site not responding. Last check: 2007-10-21)
		This chapter deals with algorithms that compute spanning subgraphs, that is they remove some edges from an input graph in order to establish a certain graph property.
		Planar subgraphs are used for graph planarization, i.e., in the SubgraphPlanarizer module.
		In the latter case, the input graph is made acyclic by reversing the edges in a maximal acyclic subgraph.
	www.ads.tuwien.ac.at /AGD/MANUAL/Computation_Subgraphs.html (82 words)

	Subgraph Construction
		Subgraph decomposition is a field in itself (see, for instance, (Bosák, 1990)), and we make no claims regarding the optimality of our approach.
		Once the current subgraph can no longer expand, new actions are calculated for any of the subgraphs that might have been affected by the expansion of previous subgraphs.
		Subgraph decomposition is not the focus of this research, although improvements can dramatically reduce the complexity of HG.
	crl.nmsu.edu /users/sb/papers/graph-topology/node6.html (976 words)

	From the Cover: Using three-dimensional microfluidic networks for solving computationally hard problems -- Chiu et al. ...
		The largest subgraph that forms a clique in A is {1,2,3} and in B, {1,3,4,5,6}.
		For simplicity, we use the terms subgraph and subset interchangeably in this paper (formally, a subset is a collection of vertices of a graph G, and a subgraph is a collection of vertices and edges of G).
		The bright circles in A are wells that represent the different subgraphs; the reservoirs that represent edges are to the left of the picture and are not shown.
	www.pnas.org /cgi/content/full/98/6/2961 (3918 words)

	Graph Theoretic Results (Site not responding. Last check: 2007-10-21)
		There are clearly 2e+1 connected subgraphs having at most 2 vertices, so the problem is to bound the number of connected subgraphs having exactly 3 vertices.
		Subgraphs are allowed to have at most one variant vertex.
		connected subgraphs having at most 3 vertices, where at most one of the vertices is a variant.
	www.ccs.neu.edu /home/kenb/key/fast/subsectionstar3_10_1.html (182 words)

	Boost Graph Library: Subgraph
		An induced subgraph is a subgraph formed by specifying a set of vertices V' and then selecting all of the edges from the original graph that connect two vertices in V'.
		Adding an edge to a subgraph causes the edge to also be added to all of its ancestors in the subgraph tree to ensure that the subgraph property is maintained.
		from the subgraph and from all of the ancestors of
	www.boost.org /libs/graph/doc/subgraph.html (1565 words)

	Graphs (Site not responding. Last check: 2007-10-21)
		The connected components of a graph are a partitioning of the graph into subgraphs such that two vertices are in the same connected component, if and only if there is a path between the vertices.
		In words, for the 2-section graph of a graphical model, two subgraphs of the 2-section graph form a decomposition of the graph with respect to a subset c of the vertices of the graph, if the graph is the union of two subgraphs and the intersection c between the two subgraphs is complete.
		a graph and its subgraphs can be decomposed recursively until all the subgraphs are complete, then the graph is decomposable.
	www.math.aau.dk /~jhb/Thesis/PartI/node58.html (415 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		To determine the significance of coherent protein subgraphs, we have conducted an experimental study in which all coherent subgraphs were identified in several protein structural families annotated in the SCOP database (Murzin et al, 1995).
		The total number of frequent subgraphs for a set of graphs grows exponentially as the average graph size increases, as graphs become denser, as the number of node and edge labels decreases and as the size of the recurring subgraphs increases (Huan et al 2003).
		The mapping q1 (p2, q2 (p1, q3(p3 represents an induced subgraph isomorphism from graph Q to P. (b) All the frequent induced subgraphs with minSupport set to be 2/3 for the graph database presented in (a).
	smi-web.stanford.edu /projects/helix/psb04/huan.doc (2136 words)

	Zoomgraph version 0
		Subgraphs let us bundle a related edges and nodes together and give them a name. You can type “sg list” to see a list of named subgraphs.
		If you have a subgraph defined with nodes in it, any node command applied to that subgraph will act on the nodes held within the subgraph.
		If the subgraph definition file includes an edge or node that is not defined in the database you will see an error.
	www.hpl.hp.com /shl/projects/graphs/doc/zg-manual.htm (3318 words)

	Subgraphs
		In applications which manipulate extremely large graphs, it is often a practical necessity to present the graph as a small, ``coarse'' graph in which certain areas of interest to the end user can be expanded to reveal finer detail.
		This subgraph contraction in LINK is hierarchical, i.e., the programmer or user can create arbitrary numbers of subgraph layers (subgraphs contracted within subgraphs).
		Once created, subgraphs may be ``opened'' without being ``dissolved.'' The user may want to view the expanded graph momentarily, then hide the subgraph again.
	dimacs.rutgers.edu /~berryj/manual/node104.html (331 words)

	aiSee: Subgraphs
		(For dynamically defined node groups, see regions.) Subgraphs and summary nodes can be drawn in a special shape and/or color so as to be easily identified (see GDL in a Nutshell).
		A subgraph is selected by clicking on one of its nodes.
		The interactive folding, boxing, clustering and wrapping operations allow more than one subgraph to be selected at the same time.
	www.aisee.com /manual/unix/24.htm (100 words)

	Response to Comment on "Network Motifs: Simple Building Blocks of Complex Networks" and "Superfamilies of Evolved and ...
		In the lattice networks, directed connections were formed at random between neighboring nodes arranged on a two-dimensional lattice (1).
		Red arrows indicate subgraphs that occur in the random-lattice network much more often than in the real network.
		These subgraphs are generally found in other variants of PA models that generate feedforward loops.
	www.sciencemag.org /cgi/content/full/305/5687/1107d (1010 words)

	[boost] [BGL] write_graphviz normal graphs vs. subgraphs w.r.t.attribute
		The handling of attributes in write_graphviz differs greatly depending on whether the graph given to write_graphviz is a subgraph or not.
		Instead, we use properties with tags vertex_attribute_t and edge_attribute_t to output attributes: the value type for these properties is a container of pairs (n,v) where n is the name of the attribute and v is the value.
		For instance, I think we should keep subgraph<>'s use of vertex_attribute_t and edge_attribute_t for the attribute list, but introduce an easy way to use values in a property map.
	www.mail-archive.com /boost@lists.boost.org/msg06844.html (267 words)

	gdea - An Algorithm for Finding Large Induced Planar Subgraphs
		Our algorithm builds up an induced planar subgraph by iteratively adding a new vertex to it, or swapping a vertex in it with one outside it, in such a way that the procedure is guaranteed to stop, and so as to preserve certain properties that allow its performance to be analysed.
		This paper presents an efficient algorithm that finds an induced planar subgraph of at least 3n/(d+1) vertices in a graph of n vertices and maximum degree d.
		This bound is sharp for d=3, in the sense that if \varepsilon>3/4 then there are graphs of maximum degree 3 with no induced planar subgraph of at least \varepsilon n vertices.
	gdea.informatik.uni-koeln.de /archive/00000422 (767 words)

	enumeration of all strongly connected subgraphs - INFORMS Online Discussion
		Topic: enumeration of all strongly connected subgraphs ([an error occurred while processing this directive])
		I am doing research on relationship of online communities with each other.
		subgraphs (i.e., a subgraph that is SCC) of a given directed graph.
	www.informs.org /ubb/Forum1/HTML/000005.html (79 words)

	Forbidden Subgraphs that Imply Hamiltonian-Connectedness (ResearchIndex)
		Also, examples will be described that determine a finite family of graphs L such that if a 3-connected graph being claw-free and L-free implies G is hamiltonian-connected, then L #L. Keywords...
		0.9: Forbidden Subgraphs, Hamiltonicity and Closure in Claw-Free..
		9 Restrictions on induced subgraphs ensuring hamiltonicity or..
	citeseer.ist.psu.edu /broersma99forbidden.html (230 words)

	Local graph alignment and motif search in biological networks -- Berg and Lässig 101 (41): 14689 -- Proceedings of ...
		subgraphs, subgraphs with increasing mutual mismatches are included.
		Nontreelike subgraphs are enumerated and node pairs i, j are binned according to w
		random subgraphs because of a prevalence of internal loops.
	www.pnas.org /cgi/content/full/101/41/14689 (4590 words)

	Record labels in subgraphs (Site not responding. Last check: 2007-10-21)
		The command displays the values of some field of the data records in subgraphs.
		The layer to be labelled and the maximum number of the labels in each neuron can be restricted by the parameters and .
		If is not given here, then a classified data, that has been connected to the graphic structure by the command setgcld, is used.
	erin.mit.jyu.fi /projects/nda/usrman.old/node141.html (134 words)

	abstract Hofstad 2004 (Site not responding. Last check: 2007-10-21)
		We study random subgraphs of finite graphs where bonds are occupied with probability p.
		This problem has attracted considerable attention in the combinatorics community, and detailed results are proven for the random graph, which is the random subgraph of the complete graph.
		At the same time, in statistical mechanics, the problem of percolation, which is equivalent to random subgraphs of infinite graphs, has inspired substantial and deep work.
	www.win.tue.nl /~amc/seminar/abstracts/hofstad.html (260 words)

	On-Line 3-Chromatic Graphs I. Triangle-Free Graphs
		On the other hand, based on the characterization of this family, all 22 forbidden subgraphs of on-line 3-colorable triangle-free graphs are determined.
		As a corollary, we obtain the 10 forbidden subgraphs of on-line 3-colorable bipartite graphs.
		The forbidden subgraphs in the finite basis characterization are on-line 4-critical, i.e., they are on-line 4-chromatic but their proper induced subgraphs are on-line 3-colorable.
	epubs.siam.org /sam-bin/dbq/article/31030 (237 words)

	Approximating minimum-size k-connected spanning subgraphs via matching (Site not responding. Last check: 2007-10-21)
		An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of a given (undirected or directed) graph G=(V,E).
		There are four versions of the problem, depending on whether G is undirected or directed, and whether the spanning subgraph is required to be k-node connected (k-NCSS) or k-edge connected (k-ECSS).
		For undirected graphs and k=2, a (deterministic) parallel NC version of the heuristic finds a 2-node connected (or a-edge connected) spanning subgraph whose size is within a factor of (1.5+/spl epsiv/) of minimum, where /spl epsiv/>0 is a constant.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/focs/1996/7594/00/7594toc.xml&DOI=10.1109/SFCS.1996.548488 (267 words)

	Complexity Digest - The Inhomogeneous Evolution of Subgraphs and Cycles in Complex Networks
		Abstract: Subgraphs and cycles are often used to characterize the local properties of complex networks.
		Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains unchanged, while the density of others increase at a rate that is determined by the network's degree distribution and clustering properties.
		This inhomogeneous evolution process, supported by direct measurements on several real networks, leads to systematic shifts in the overall subgraph spectrum and to an inevitable overrepresentation of some subgraphs and cycles.
	www.comdig.org /article.php?id_article=20292 (137 words)

	[No title]
		Then there exists vi, vj, iEMBED Equation.3 j such that if H — vi is replaced by H — vj then the resulting family of subgraphs is not a legitimate deck, and (ii) not all subgraphs in the family are isomorphic, and (iii) at least one of these subgraphs is connected.
		Here the k subgraphs of EMBED Equation.3 which form the family S, must come by deleting a vertex from the component F. This implies that F and H share the common subdeck H1, H2, , Hk.
		Consider when the component H is (i) not regular and not quasi-regular, or (ii) regular or quasi-regular Case(i) H not regular, H not quasi-regular Choose c subgraphs of H as in the Lemma 5.
	staff.um.edu.mt /jlau/research/rec_no.doc (1581 words)

	CiteULike: Subgraphs and network motifs in geometric networks. (Site not responding. Last check: 2007-10-21)
		To understand the origin of the network motifs in these networks, it is important to study the subgraphs and network motifs that arise solely from geometric constraints.
		To address this, we analyze geometric network models, in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes.
		Scaling rules for scaling of subgraph numbers with system size, lattice dimension, and interaction range are given.
	www.citeulike.org /user/korakot/article/158532 (312 words)

	[GRAPE] 7 Vertex-Colouring and Complete Subgraphs (Site not responding. Last check: 2007-10-21)
		can also be used to determine the complete subgraphs with given vertex-weight sum in a vertex-weighted graph indexvertex-weighted graph.
		, which can be used to compute the maximal complete subgraphs of given size, and can also be used to determine the (maximal or otherwise) complete subgraphs with given vertex-weight sum in a vertex-weighted graph.
		A complete subgraph is represented by its vertex-set.
	www.gap-system.org /Manuals/pkg/grape/htm/CHAP007.htm (400 words)

	Isomorphisms (Site not responding. Last check: 2007-10-21)
		A subgraph is the restriction of a graph to a subset of its points.
		In other words, the subgraphs determine the graph.
		This breaks down for v = 2, since a single edge has the same subgraphs as two disconnected points.
	www.mathreference.com /gph,iso.html (102 words)

	Definition (Site not responding. Last check: 2007-10-21)
		an induced subgraph of a graph is obtained by deleting some vertices and all edges incident with one or two of the deleted vertices.
		A class G of graphs is closed under subgraphs if every induced subgraph of any member of G is again in G.
		A biclique is any inclusion-maximal induced complete bipartite subgraph (where it is even allowed that one partition class is empty).
	www.math.uni-hamburg.de /spag/gd/mitarbeiter/prisner/Pris/Def.html (443 words)

	Properties of Optimum Subgraphs
		In this section we establish a fundamental property of optimum subgraphs for MPWPSP.
		This helps to reduce the search space of planar subgraphs which may be candidates for an optimum solution.
		Hence, G has a planar subgraph with 3n-6 edges which is a triangulation.
	www.coe.montana.edu /ie/faculty/emooney/pubs/cie96/node4.html (190 words)

	Seminários de Teoria da Computação e Combinatória - DCC IME USP (Site not responding. Last check: 2007-10-21)
		Abstract: Consider the minimum $k$-edge-connected spanning subgraph problem: given a positive integer $k$ and a $k$-edge-connected graph $G$, find a $k$-edge-connected spanning subgraph of $G$ with minimum number of edges.
		We improve their analysis, proving that the performance ratio of their algorithm is smaller than 1.7 for large enough $k$, and that it is at most 1.75 for all $k$.
		Last, we show that the minimum 2-edge-connected spanning subgraph problem is MAX SNP-hard.
	www.ime.usp.br /~cris/gcomb/seminarios/abstracts/cris/kconnec.html (139 words)

	SimFinder (Site not responding. Last check: 2007-10-21)
		The upper limit on the size of subgraphs inside similarity statements; if 0, there is no upper limit.
		- the initial size of the subgraphs in the population.
		The useCounter tells how many Subgraphs of the SimilarityStatements in the population the vertice can be found in.
	www.ofai.at /~soren.madsen/daimi/simfinder/doc/SimFinder.html (684 words)

	Experiments on outerplanar subgraphs (Site not responding. Last check: 2007-10-21)
		Determining the maximum outerplanar subgraph of a given graph is known to be NP-complete.
		In the literature there are no earlier experiments on approximating the maximum outerplanar subgraph problem.
		The main experimental result is that simulated annealing with initial solution taken from the greedy cactus-tree heuristic yields the best known approximations for the maximum outerplanar subgraph problem.
	www.cs.uta.fi /~tp/max_outerplanar (194 words)

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