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Topic: Dicycle graph

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Eulerian path

Graph theory

Isomorphism class

Isomorphism

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	Eulerian path - Wikipedia, the free encyclopedia
		Carl Hierholzer published the first complete characterization of Eulerian graphs in 1873, by proving that in fact the Eulerian graphs are exactly the graphs which are connected and where every vertex has an even degree.
		An undirected graph is traversable iff it is connected and at most two vertices in the graph are of odd degree.
		A directed graph version of the Eulerian cycle algorithm can be obtained in a similar fashion, except that the even degree condition is replaced by an equal in- and out-degrees condition.
	www.wikipedia.org /wiki/Unicursal (719 words)

	Eulerian path
		An undirected graph is Eulerian iff it can be constructed using edge disjunct cycle graphs.
		A directed graph is Eulerian iff it is diconnected and every vertex has equal in degree and out degree.
		A directed graph is Eulerian iff it can be constructed using arc disjunct dicycle graphs.
	www.arikah.net /encyclopedia/Eulerian_path (763 words)

	Eulerian path (Site not responding. Last check: 2007-10-16)
		Mathematically the problem can be stated like this: :Given the graph on the right, is it possible to construct a cycle (a path starting and ending on the same vertex) which visits each edge exactly once.
		In 1873 Hierholzer published the first complete characterization of eulerian graphs by proving that in fact the eulerian graphs are exactly the graphs where every vertex has an even degree.
		A directed graph version of Eulerian cycle result and algorithm can be obtained in a similar fashion except that the even degree condition is replaced by an equal in- and out-degrees condition.
	eulerian-path.encyc.dyndns.dk (634 words)

	Articles - Cycle graph (Site not responding. Last check: 2007-10-16)
		In graph theory, a cycle graph or cycle is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.
		Any graph with a subgraph that is a cycle is not a tree.
		A directed cycle graph is a directed version of a cycle graph, with all the edges being oriented in same direction.
	www.wadso.com /articles/Dicycle_graph (331 words)

	Information on A. Yeo's preprints
		This is a generalization of the alternating cycle problem in 2-edge-coloured graphs (proved to be polynomial time solvable) and the even dicycle problem (the complexity is not known yet).
		These are those graphs whose vertices can be circularly enumerated so that either the neighbourhood or the closed neighbourhood of each vertex forms an interval in the enumeration.
		We show how to reduce the problem of recognizing general round graphs to the problem of determining whether a weakly triangulated graph is round (a problem which is still open).
	www.brics.dk /~yeo/pre_info.html (6149 words)

	Directed acyclic graph - Enpsychlopedia
		In mathematics, a directed acyclic graph, also called a dag or DAG, is a directed graph with no directed cycles; that is, for any vertex v, there is no directed path starting and ending on v.
		DAGs appear in models where it doesn't make sense for a vertex to have a path to itself; for example, if an edge u→v indicates that v is a part of u, such a path would indicate that u is a part of itself, which is impossible.
		Every directed acyclic graph has a topological sort, an ordering of the vertices such that each vertex comes before all vertices it has edges to.
	psychcentral.com /psypsych/Directed_acyclic_graph (464 words)

	Glossary of Signed and Gain Graphs and Allied Areas
		These definitions about graphs are intended not to be a glossary of graph theory but to clarify the special usages appropriate to signed, gain, and biased graphs.
		» A connected graph consisting of two vertex-disjoint polygons and a minimal (not necessarily minimum-length) connecting path (this is a loose handcuff), or of two polygons that meet at a single vertex (a tight handcuff or figure eight).
		In a connected graph embedded in a surface a plaquette is a region boundary; in a cubic lattice graph it is a square bounding one face of an elementary cube of the lattice.
	www.combinatorics.org /Surveys/ds9.html (10769 words)

	MFCS '04 Accepted Papers (Site not responding. Last check: 2007-10-16)
		On the algorithmic side, by showing that an augmented grid is the prototype bounded-genus graph, we generalize and simplify many existing algorithms for such problems in graph classes excluding a minor.
		Then, we consider bounded degree graphs and prove that we are able to distribute an information among all nodes in $O(D)$ steps, where $D$ denotes the diameter of the graph.
		Abstract: We study the on-line versions of two fundamental graph problems, maximum independent set and minimum coloring, for the case of {\em disk graphs} which are graphs resulting from intersections of disks on the plane.
	mfcs.mff.cuni.cz /papers.html (7486 words)

	Vega - User Manual (Site not responding. Last check: 2007-10-16)
		The valence of each vertex of correspondent graph is not greater than 3 and not lower than 2 and so a new face can be attached only to vertices of valence 2.
		Generalized spiral code is a list of pairs {m,n} where m (m>=3) is number of vertices of a new face and n (n>=1) is a position where to attach a new face.
		A result is a list with two elements where the first one is an adjacency list representation (it is a list of lists) for the correspondent graph and the second is a list of vertices of the outer face of the correspondent Schlegel diagram.
	vega.ijp.si /htmldoc/manual/USER.HTM (4176 words)

	Minimum Weight Dipaths (Site not responding. Last check: 2007-10-16)
		Note also that a minimum weight v-w diwalk need not in general be the same as a minimum weight v-w dipath.
		If G does contain a negative weight dicycle, then then for some pair of vertices s and t, there exists an s-t diwalk with arbitrarily large negative weight.
		If G has no dicycles (note that the underlying undirected graph may have cycles), then we can employ a clever labeling scheme so that for any edge, the label at the tail is less than the label at the head.
	www.ms.uky.edu /~sills/webprelim/sec15.html (409 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		] A graph in which a direction is shown for every arc.
		] A directed graph in which each arc is assigned a unique nonnegative integer called its weight.
		vn, in a directed graph such that there is an arc from vi to vi+1 for i = 1, 2,
	www.accessscience.com /Dictionary/D/D22/DictD22.html (2251 words)

	On Integrality, Stability and Composition of Dicycle Packings and Covers (Site not responding. Last check: 2007-10-16)
		Given a digraph $D$, the {\bf minimum integral dicycle cover problem} (known also as the {\bf minimum feedback arc set problem}) is to find a minimum set of arcs that intersects every dicycle; the {\bf maximum integral dicycle packing problem} is to find a maximum set of pairwise arc disjoint dicycles.
		We also observe that if $\nu=\nu^$ holds for each piece, where $\nu^$ ($\nu$) is the value of a maximum (integral) dicycle packing, then the stability property holds as well.
		In particular, we use the methods obtained to extend an $O(n^3)$ algorithm for finding a minimum integral dicycle cover and an $O(n^4)$ algorithm for finding a maximum integral dicycle packing from planar digraphs to $K_{3,3}$-free digraphs (i.e., digraphs not containing any subdivision of $K_{3,3}$).
	roso.epfl.ch /ismp97/ismp_abs_894.html (259 words)

	Citations: New Scaling Algorithms for the Assignment and Minimum Cycle Mean Problems - Orlin, Ahuja (ResearchIndex)
		Using the distance graph reformulation, the feasibility of such a system with M weak inequalities on N variables, with sum of absolute values of arc weights C, can be decided in O(min(NM; p NM log NC) time
		Deciding if a UCO graph with di#erence constraints has a realization can be done in O(min(n 3, n 2 1 2 log nC) time.
		Feder and Motwani [6] give a graph compression technique that combines with the algorithm of Dinitz to yield an O(p nm log(n 2 =m) log n) algorithm.
	citeseer.ist.psu.edu /context/599032/0 (2398 words)

	Class sg2.graph.Graph (Site not responding. Last check: 2007-10-16)
		Factory method that construct an emtpy graph on n vertices.
		Factory method that constructs K graph on n vertices.
		Factory method that constructs filled bipartite graph on n1 and n2 vertices K(n1,n2).
	www.ijp.si /vega/Gallery/HTML/s/sg2.graph.Graph.html (270 words)

	Nathaniel Dean, Scholarly Interests, Rice University (Site not responding. Last check: 2007-10-16)
		Nathaniel Dean, "What is the smallest number of dicycles in a dicycle decomposition of an eulerian digraph?" J.
		Nathaniel Dean, "Dicycle decomposition of eulerian digraphs," Congressus Numerantium, 64 (1988): 89-94.
		Nathaniel Dean, P. Fraisse, "A degree condition for the circumference of a graph," J.
	dacnet.rice.edu /faculty?FDSID=816 (1064 words)

	CU-Denver Department of Mathematics Events
		A digraph whose underlying graph is a path, cycle or nova will be called respectively a dipath, dicycle or dinova.
		Let m(D) denote the number of minimial king sets of D and let M(D) denote the minimum number of vertices in a king set of D. We give an algorithm for finding m(D) and for finding M(D) when D is either a dipath or a dicycle.
		We also show how to compute M(D) if D is a dinova, and we give a lower bound for m(D) if D is a dinova.
	www-math.cudenver.edu /events/QueryEvent.php?eid=264 (135 words)

	Glossary of Signed and Gain Graphs and Allied Areas
		In a signed or gain graph (thus, with X implicitly = sign or gain group), a state is a function V -> the group.
		» Matroid whose circuits are the polygons of the graph (for an ordinary graph).
		The graphs are those of the carbon skeleta.
	www.math.binghamton.edu /zaslav/Bsg/glossary.html (10726 words)

	Minimization of Setup-Times for Printing Machines (Site not responding. Last check: 2007-10-16)
		The setup time together with the printing time of the second job of this ordered pair forms the cost of an arc in a graph of possible transitions.
		A solution consists of one directed dicycle for each special node so that all dicycles cover all nodes of the graph exactly once.
		We consider a solution optimal if the longest of its dicycles is as short as possible.
	www.zib.de /projects/production-planning/printing/desc.en.html (522 words)

	DC MetaData for: On Algebraic Properties in Shop Scheduling Problems (Site not responding. Last check: 2007-10-16)
		Abstract: In this paper investigations in graph theory, algebra and scheduling theory
		is reduced to the existence of fundamental dicycles in G(MO,JO).
		The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.
	www.math.uni-magdeburg.de /preprints/shadows/01-08report.html (222 words)

	Citations: the integral dicycle packings and covers and the linear ordering polytope - Nutov, Penn (ResearchIndex)
		Lemma 2.1 (10] If D is a facet defining digraph then D satisfies the following necessary conditions: D is diconnected; D is 2 connected; the degree of each node in D is at least 3; Lemma 2.
		) If D is a facet defining digraph then D is not K 3;3 free (a digraph is K 3;3 free if its underlying graph does not contain as a subgraph the graph K 3;3 or any of its subdivisions) From Lemma 2.
		Nutov, M. Penn, On the integral dicycle packings and covers and the linear ordering polytope, Discrete Applied Mathematics, 60 (1995) 293-309.
	citeseer.ist.psu.edu /context/615623/0 (710 words)

	Nathaniel Dean - Mathematicians of the African Diaspora
		Higher dimensional representations of graphs (w/ A. Buja, M. Littman and D. Swayne) Technical Report 95-47, DIMACS, Piscataway, NJ (1995).
		Dicycle decomposition of eulerian digraphs Congressus Numerantium, 64 (1988) 89-94.
		Longest cycles in 3-connected graphs contain three contractible edges J. Graph Theory, 13 (1989) 17-21.
	www.math.buffalo.edu /mad/PEEPS/dean_nathaniel.html (477 words)

	[No title]
		Huang (Rockford, Illinois) On the Perturbation of the Least Squares Solutions in Hilbert Spaces 487 Javad Faghih-Habibi (New Concord, Ohio) The Spherical Gap of the Graph of a Linear Transformation 501 A.
		Farid (Calgary, Alberta, Canada) Criteria for Invertibility of Diagonally Dominant Matrices 63 Ji-guang Sun (Umea, Sweden) On Perturbation Bounds for the QR Factorization 95 Janez Mrcun (Ljubljana, Slovenija) Lipschitz Spectrum Preserving Mappings on Algebras of Matrices 113 J.
		McMorris (Louisville, Kentucky), and Fred S. Roberts (New Brunswick, New Jersey) p-Competition Graphs 167 Steve Kirkland (Regina, Saskatchewan, Canada) Spectral Radii of Tournament Matrices Whose Graphs Are Related by an Arc Reversal 179 J.
	www.math.technion.ac.il /iic/LAA.INDEX (5113 words)

	Cycle graph - Definition, explanation
		In graph theory, a cycle graph or circle graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.
		Cycle graph (group) — using cycle graphs to illustrate the structure of small finite groups
		If you know or can find out more about its subject, you can help by expanding it (select the [ "Edit this page"] link).
	www.calsky.com /lexikon/en/txt/c/cy/cycle_graph.php (343 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		147-180 Shi, Ronghua Path polynomials of a graph.
		245-263 Haemers, Willem H. Distance-regularity and the spectrum of graphs.
		Hadjidimos, A. Yeyios Page 303 Minimum Rank Matrices with Prescribed Graph P.
	hermite.cii.fc.ul.pt /iic/LAA.96 (2033 words)

	Details of A. Yeo's publications
		Total domination of graphs and small transversals of hypergraphs
		The number of pancyclic arcs in a k-strong tournament.
		Relationships between total domination, order, size and maximum degree of graphs
	www.cs.rhul.ac.uk /home/anders/pre_info.html (6289 words)

	Journal of Combinatorial Optimization, Volume 4
		Hiroshi Nagamochi, Shigeki Katayama, Toshihide Ibaraki: A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs.
		Zeev Nutov, Michal Penn: On Integrality, Stability and Composition of Dicycle Packings and Covers.
		Jieliang Zhou, Patrick W. Dymond, Xiaotie Deng: Graph Algorithms with Small Communication Costs.
	www.informatik.uni-trier.de /~ley/db/journals/jco/jco4.html (306 words)

	Linear Algebra and its Applications
		A Characterization of Graphs With Interval Two-Step Graphs
		Singular Graph and Extension of Jordan Chains of an M-Matrix 167
		Graph Theoretic Aspects of Maximizing the Spectral Radius of Nonnegative Matrices
	www.numerik.uni-kiel.de /journals/laa.html (5259 words)

	Cycle graph (Site not responding. Last check: 2007-10-16)
		Amazon.com reports that it carries about 684 items relevant to Cycle graph
		You can click on this message to see their list of those items.
		Sorry, no screened links relevant to Cycle graph were found:
	www.omniknow.com /common/wiki.php?in=en&term=Directed_cycle (465 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		Consequently, a wide variety of formal models will be discussed and the term "mathematical model" will include classical models such as differential or difference equations, Markov processes, ARMA models as well as more recent approaches such as Bond graphs or Petri nets.
		The topics to be discussed will include - modelling theory - processes and methods for model formulation, identification, development, reduction and validation etc. (incl.
		TOPICS: Combinatorial optimization and algorithms on discrete structures, Extremal problems in posets, Design theory, Coding theory, Cryptography, Graph theory, Complexity theory and related topics.
	www.scicomp.uni-erlangen.de /Digest/v96n10 (13334 words)

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